To install many hard drives in a computer you need enough of five things:
1. hard drives;
2. unused ports on the mobo to plug into - usually SATA or SATA II;
3. spaces in the case for physical mounting;
4. power supply connectors from the PSU; and
5. data connection cables from HDD's to mobo ports.
On item 3, even if you don't seem to have enough HDD mounting slots in the regular "cage" area, remember that HDD's also can be mounted in the 3½" slots usually used for a floppy drive - you just do not remove the case front cover for access. With an adapter, you even can mount a 3½" HDD in a wider 5¼" slot usually used for an optical drive.
On item 4, if there are not enough power supply connectors for all the SATA drives on the wires coming out of the PSU, you can make more two ways. One is simply to use adapters that convert one SATA power connector to two. The other is to use a different adapter that converts a 4-pin Molex power connector to a SATA power connector.
To use multiple drives you do not need to use RAID, depending on HOW you want the drives to be used. If it is OK to simply have four drives, each with its own drive letter and containing about one quarter of your files, no problem - just use them that way. This does have real advantages for backup management, speed of finding files, etc.
If you really want to have all your drives appear to be one large volume, then a form of RAID is the way. But study up on RAID - you need to understand what you get and what you risk.
The simplest (and not really a RAID system, but often included in a chipset feature with RAID) is called JBOD or Spanning. JBOD stands for Just a Bunch of Disks. It organizes several HDD physical units into what appears to be one large continuous disk. The capacity is simply the sum of the component units.
RAID0 can organize two or more HDD units to appear to be only one disk, and it does it by spreading successive fragments of every file over all its disks. It also gives you the full capacity of the sum of its components, and it may be a little faster in performance. BUT the downside is that the risk of total data loss is higher in RAID0 than any other disk system. This is because ALL of the component disk units MUST be functioning. If ANY ONE HDD unit fails, all of the array's data is lost because EVERY file has its data spread over ALL of the HDD units.
RAID1 is a mirroring system. Typically constructed from only 2 HDD units, it uses the second as a complete duplicate of the first at all times. So even if one develops a flaw, the other is fully functional and it allows you time to fix the faulty one and rebuild the array. However, this means you only get half your space - two 2TB units give you only 2TB of space.
RAID5 uses 3 or more HDD's (the classic is 5 HDD's) and spreads the data over all of them, but adds extra data checking information so that a failure of any one HDD in the array means that, with time to do it, ALL of the data can be regenerated from the good remaining information after the faulty unit is replaced. The creation and storage of the extra info means that the system makes available for use only about 80% of the component drives' capacity. Moreover, the extra work involved slows down system performance. This is typically the sort of system used in large professional servers.
There are other more advanced RAID systems that are even more fault-tolerant and more complex with a larger impact on "wasted space" on the HDD units.
No matter what system you choose, you REALLY need to look also at a back up system. You need a system that can accommodate all of your data, with periodic updates of most recent changes. Ideally it needs to be a system that allows you to remove the backup device and transport it to an offsite safe storage location. Because of the risk factors associated with RAID0 (especially when using more than 2 HDD's in the array!) some advise that backups are extra important for RAID0 users. However, they are important for ALL users who never want to lose their data.
RAID also has a problem with recovery from certain types of failure. The exact details of how data is organized and stored in a RAID system is not standardized over all devices. Hence a set of RAID disks written with one controller system probably will NOT be readable by a different controller. So if the equipment that fails is your RAID controller or your motherboard you must search for and replace it with an almost identical unit so that your disks can be used by the replacement system.
Of all of these options, the most secure in terms of ability to recover data from some failure is to use several individual HDD's as separate drives, PLUS use a good data backup system. RAID systems certainly have advantages to offer; you need to learn about them and decide whether any of them actually does give you features you find valuable. But never use a RAID system as a substitute for a good regularly-used backup system.