It's true, building your own PC is easier than it looks. You still have to be careful about static and delicate CPU chips etc. but thats fairly obvious. I'll give you some guidelines for a gaming build on this budget.
CPU: Intel Core i5-2500k
Best gaming CPU around, awesome value and great for overclocking. If you don't want to overclock however, get a cheaper i5-2400.
RAM: 2x2GB or 2x4GB 1600Mhz DDR3
4GB is plenty for games at the moment but RAM is cheap so a lot of people just get 8GB anyway. Also be sure to go with a decent brand such as Corsair, GSkill, OCZ etc. Higher frequency and lower CAS latency is best, i wouldn't bother getting any faster than 1600Mhz though.
Motherboard:
If you don't want to overclock or SLI/Crossfire then you can get pretty much any socket 1155 motherboard so long as it fits your RAM and case. If you want to overclock but not crossfire (which i reccommend) then the ASUS P8P67 or equivalent is a good choice. If you want to SLI/Crossfire and overclock (or just SLI/Crossfire) then the ASUS P8P67-PRO or equivalent is a good choice. As for motherboard manufacturers, most of them are pretty decent but if unsure i'd stick to ASUS, ASRock, MSI and Foxconn. They've always been good to me at least.
Graphics:
This depends on how much cash you have as you can never really have too good a graphics card for gaming but on your budget i would aim for something like GTX 570, HD 6970 or GTX 560Ti. One thing to mention though, if youre playing in high resolutions then more graphics memory is best.
Power Supply:
This depends on the parts you choose, whether you want to overclock/SLI and how many USB devices you have. With no overclocking and 1 GPU i'd say ~550W, with heavy overclocking i'd say 600W. With Dual GPU's and/or lots of USB devices i'd go for something like 750-850W. Also this is the place you definitely want to go with a decent brand such as Antec, Corsair, OCZ, Cooler Master, XFX, Seasonic. Also try to get a modular PSU if you can, it means less wires which means more airflow and less mess inside your case.
Hard Drive:
Depending how much you spend on the rest of your build, you might be able to afford a ~60-80GB SSD to use as your boot drive but if you don't want to or you cant afford it, i reccommend either the Samsung Spinpoint F3 or the Western Digital Caviar Black Series Hard Drives. If you do get the SSD then you can afford to get a cheaper HDD such as a Seagate Barracuda as your storage Drive.
Case:
With cases a lot of it is personal preference but for gaming the HAF 912/922/932/X and the Antec 300/902/1200 are decent. You should get something that is nice and big with decent airflow and cable management. It would be a good idea to look at some reviews.
CPU Cooler:
You only need to bother with a CPU cooler if you want to overclock, if it's a minor overclock then the Cooler Master Hyper 212+ is a popular choice. If you want something more heavy duty then have a look at the higher end Scythe, Noctua and Cooler Master coolers. I would reccommend sticking with air cooling over water cooling.
Hope this helped, let me know if you have any more questions.
EDIT: Forgot to say, theres a really great guide on here for building your own PC, i'd say stick to that and you cant go wrong.
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