I'm going to write about the automatic fan control systems built into mobos. While you can buy separate third-party fan controller modules to mount in the front of your case and MANUALLY set the speeds of each of your fans, I believe the pre-programmed systems in mobos that do adjust fan speeds according to measured temperatures automatically are much better. Note that ALL of these are really TEMPERATURE control systems. That is, their focus is the actual measured TEMPERATURE at a sensor, and they manipulate the speed of a fan aimed at the heat site to keep the temperature at a target value. In all cases, the mobo makers have pre-programmed their BIOS with info on the proper target temperatures for each of the many devices that might be connected or plugged in, and what the fan controls should do for them. Normally they also offer you for each header three other options: fixed slow speed for quiet operation (but reduced cooling!), fixed full speed (max cooling and noise), and custom fan speed curves you can set yourself. I advise NOT using the custom curve tool until you have some experience with your system. The default automatic settings usually work very well.
There are two "groups" of fan control systems on a mobo, There is always one for the CPU chip connected to the CPU_FAN header, and maybe to others like a CPU_OPT or something. On these almost always the only choice for which sensor is used as its guide is the one inside the CPU chip; its signal is fed out to the mobo on one chip pin. Then there are several SYS_FAN or CHA_FAN headers intended for use with case ventilation fans. Although they MAY all be linked to a single control loop, most often each can be configured individually. Most commonly these all are guided by a single temperature sensor built into the mobo and positioned wherever the designer felt was the best sensor location. However, many mobos now have more than one sensor on the mobo, and the allow you to choose which of these (or even choose the sensor inside the CPU) to use to guide each header individually. This allow you, for example, to decide to position a fan to blow onto a particular mobo key component and use the temp sensor in that location to guide that fan.
You MAY encounter two other types of fan headers. You still see some called PWR_FAN. They are no longer popular. Their design was to cooperate with a feature in some PSU units. PSU fans may always run at full speed, but more commonly today the PSU itself manages its own fan speed according to its own internal temperature. Some PSU's had a set of three wires ending in a female fan connector just like a 3-pin fan's, and this can plug into a mobo PWR_FAN header if you have one. The only thing this does is communicate the PSU fan's speed to the mobo so it can be displayed for you. There is NO attempt by the mobo to control that PSU fan. In many cases the mobo makers have fitted this header with a fixed Ground and +12 VDC supply on Pins 1 and 2, like a 3-pin fan header, so that it can be used as an uncontrolled power supply for a fan if you do not need it for those special leads from the PSU. But since it has no control ability, I advise not to do that. You may also see a mobo header called PUMP or something similar. Usually it is fitted to supply a constant 12 VDC on Pins 1 and 2 for a pump in a liquid-cooling system for your CPU, because many such systems are designed to have their pump run full speed all the time.
Computer fans come in two main types, each in several sizes. (The sizes are the length of one side of the square frame of the fan.) The older type has three wires from the motor to a female connector (with holes) that has two ridges on one side, just outside the three holes' locations. The male mobo header has a plastic "tongue" sticking up beside its three pins, and the ridges on the fan connector slide around this to guarantee you can only connect them one way. The wires are Black for Pin #1 (Ground), Red for Pin #2 (+VDC supply), and Yellow for Pin #3 (fan speed.) The motor generates the fan speed signal as a pulse series (two pulses per revolution) sent back to the mobo on Pin #3 for counting and display. Although this is NOT used for speed control, it IS used to monitor the fan for failure to turn. To control the speed of this fan type, the mobo alters the voltage supplied on Pin #2 from 12 VDC (full speed) down to about 5 VDC min. Any lower voltage may cause the fan to stall and fail to re-start until the mobo jolts it with a higher signal to get it going. At start-up (boot time) the mobo always sends out the full 12 VDC for a few seconds to be sure the fan starts up and goes on about its POST self-checks. After a short time it finishes that and reads the speed signal (ensuring it is working) and the target temperature sensor, and then adjusts the fan voltage down to what is necessary to keep temperature on target. Thereafter it changes the voltage according to the temperature sensor readings.
The newer 4-pin fans have a different design for how they are powered and controlled.The female connector is a little wider with a fourth hole just beyond the two ridges on the side, and the mobo male header likewise has a matching fourth pin. The connector designs mechanically allow both types of female connectors to plug into either type of male connector. Electrically the signals are similar but changed in two places. Ground (Pin 1) and Speed (Pin 3) are exactly the same. Pin #2 carries a fixed +12 VDC supply (does not vary), and Pin #4 carries the new PWM signal. Inside the fan motor there is a small chip that uses the PWM signal to modify the flow of current from the +12 VDC supply line though the motor windings to achieve speed control.
Thus we now have two different methods for controlling the speed of a fan motor, and the two design families have SOME compatibility. The older method for 3-pin fans is called Voltage Control Mode, aka DC Mode. The newer method is called PWM Mode. If you MIX items, there are two possible "mis-matches" with these results. A 3-pin fan on a PWM Mode header will always run at full speed, yielding good cooling, but just no control. It always receives the fixed +12 VDC supply on Pin #2, and it never receives the PWM signal from Pin #4 because it cannot use it, anyway. The other way - a 4-pin fan on a header using Voltage Control Mode - DOES result in controlled fan speed, although not quite as well technically as the "proper" PWM Mode control. In this case, the fan motor never gets a PWM signal from Pin #4 because the mobo is not sending it, so it cannot modify the voltage supplied on Pin #2. BUT that voltage IS being reduced by the mobo to change fan speed, so it works.
What is being done now on most mobos can be confusing. Almost all are using 4-pin male connectors for all headers, BUT the MODE that they use for control can vary. Some use only the new PWM 4-pin Mode. Some use only the older Voltage Control Mode and ignore the 4th pin. Some allow you to set which Mode is used manually for each header in BIOS Setup. Some claim that each header can detect which fan type has been plugged in and automatically change their Mode according to that. But note that there is a possible "cheat" there: if the mobo header uses only Voltage Control Mode, it CAN control either fan type, because the new 4-pin fans CAN be controlled by a 3-pin header. This becomes a problem only when using a fan Hub (later) to connect several fans to a single header, because a fan Hub MUST have a PWM signal to work.
There's a third fan type you may encounter. It comes with a connector on its wires that is much wider - about 3/4" wide with space for four round pins in a shroud - called a male 4-pin Molex connector. This mates with a female connector directly from the PSU. That PSU female output was originally used to supply 5V and 12 V DC power to IDE hard drives, optical drives, etc., and it became popular for other items. So a fan can be connected that way, often using a connector that has only two of its four pins because it only needs to connect to the +12 VDC part. This type of fan can only run at full speed with no control, and it cannot report its speed to the mobo - it has no connection there. There is also a variation on that. Some such fans come with BOTH a male 4-pin Molex AND a female 3-pin fan connector on their wires so you can use it with EITHER type of connection, but NOT BOTH.
Most mobo fan headers can supply up to 1.0 A current in total to all fans connected to that one header. This allows you to use either a SPLITTER or a HUB to connect two or more fans to the same header, subject to that limit. In doing so you must look up the specs of the fan and note the max current it uses. Many now range from 0.1 A to 0.3 A. However, be careful with some LED fans. Many of the older simpler types merely have LED's added in parallel to the motor and share whatever power supply it gets, thus increasing the current load of that fan, so check the specs!
SPLITTERS and HUBS are different devices. A SPLITTER merely connects all its fans in parallel to the power supplied from the mobo header. It has one arm with a female connector that plugs into a mobo header. It has two or more arms (or headers on a board) with pins to plug in the fans. It has no other arm types. Thus the limit on current available from the header is important. A Splitter may be either 3-pin or 4-pin, and you can connect either fan type to either Splitter type. It is becoming very common to use only 4-pin splitters no matter what fan type you have, because they will work just fine. A mobo can accept from its fan(s) the speed pulse signal (for pulse counting) from only ONE fan - two or more such signals is confusing yielding wildly varying erroneous readings. So any proper Splitter will connect to its mobo header the speed line from only ONE of its fans, and ignore all the others. The same rule applies to Hubs. IF you use a Splitter (or Hub) to connect more than one thing to the CPU_FAN header, it is important that the one signal fed back to that header IS the key cooling element for cooling of the CPU. (In cases of liquid cooler systems, follow the maker's instructions.) That is because many mobos give special close attention to the speed signal of the CPU cooler and, if it fails or is missing, will send out a quick warning of failure, then shut down the entire system to prevent damage from overheating, without even waiting to the CPU internal temperature to run high. It may also refuse to allow the system to boot if there is no CPU cooler signal there. So that header MUST receive a fan speed signal, and it REALLY should be the actual CPU cooler and not something else!
A HUB is different in a special way. It may appear to be a collection of wire arms, a circuit board, or a closed box. In addition to the two cable arm types of Splitters, it has one extra arm that must plug into a power output (either 4-pin Molex or SATA) from the PSU. ALL power for the fans on a Hub comes from the PSU, thus avoiding the limit of what a mobo header can provide. For almost all HUBS, the unit supplies +12 VDC Power and Ground connections from the PSU, sends back to the mobo header the speed of ONE fan, and merely connects the PWM signal from the mobo header to all of its fans. This means that ALL of the fans used with the Hub MUST be of the 4-pin design so they can use that PWM signal to control themselves. There are one or two Hubs on the market now that are exceptions to that rule because they use the PWM signal differently and change the control MODE used on their output ports.
OP, that's a lot of info to digest in one blast. To help apply that to your system exactly, post back here what mobo and exact model number you have. Post also case fan details - how many, what maker and model of each - and we can look up all the specs and zoom in on how you can make it all work.