As you can see in the picture they provided red/black wires for power. On your typical 4-pin molex power connector you will have Yellow (12V+), two Black (Ground), and one Red (5V+). Connect Red to Red and Black to Black and you should be good to go. If your power supply has all black or sleeved wires then you will want to use this diagram:
http://www.smpspowersupply.com/ATX-connectors.JPG
Take note of the notches. I want to stress that the LED strip you have chosen is 5V, some RGB systems are based around 12V, so be very careful later on.
The the 3 remaining wires go to the controller for setting the color. If you happen to have a 5-volt RGB compatible motherboard you could also hook it up direct I believe, but that will mean splicing it into a 4/5/6 pin header. Places like Moddiy might have adapters for that, or they may offer a superior alternative to the Amazon listing.
As for directly connecting the wires. You can get connectors like these below(Not a recommendation, just something similar to this)
and just cut them with snips and use butt type crimp connectors, wire nuts, solder, or for the dangerous, just twist the wires together and tape.
https://www.amazon.com/Computer-Molex-Power-Supply-Splitter/dp/B008KCHECW/ref=sr_1_6?ie=UTF8&qid=1529357395&sr=8-6&keywords=molex+4+pin+y+splitter
Or if you happen to have some old molex powered fans or other adapters you aren't using (GPUs often come with some, but you might have to move the pins around)