It's fairly simple to do, just takes a little time. Basically what you want to do is set a budget. This can vary greatly on where you live, prices are 30-50% higher here than in the U.S for example. So I'm going to pretty much use US prices for that reason. You can then compare prices yourself and see where you stand.
Consider what you need. Do you have a case, mouse, keyboard, monitor? Then you likely don't need to spend any money on that.
So pretty much the only components you need are : Motherboard, Processor, Video Card, RAM modules and a Power Source (you might be able to use an older one if it's output is good enough).
Motherboard. You can get away with a good mobo at around 100$ (http://www.amazon.com/ASRock-Z68-PRO3-GEN3-Intel/dp/B005N5Q2MW/ref=sr_1_5?s=electronics&ie=UTF8&qid=1327975283&sr=1-5). This will give you good OC'ing, good stability and good future proofing (PCIE 3.0). Other than that it's pretty barebone and comes with no fripperies. Since you are no pro, you won't really need any super-advanced OC features that come with the top of the line mobos, and middle line stuff will mostly just give you more LAN/USB/SATA ports and stuff you don't really need. I have to mention that not every 100$ mobo will do, ASROCK generally give you the best bet, since they cut down on "optional stuff" to boost the quality of stuff you need.
Processor. Around 200$ is more than enough. http://www.amazon.com/Intel-BOX80623I52500K-Core-i5-2500K-Processor/dp/B004EBUXHQ/ref=pd_vtp_e_1 for example is more than powerful enough to run ANY game without breaking a sweat. It's also very easy to OC (literally a few mouse clicks) and safe too. You can get a processor that will run anything (talking max detail here) for as low as 100$ and it still won't break a sweat. In the interest of futureproofing and having a more versatile PC, let's go for the 200$ option.
Video Card. This is probably where you want to spend most money. A 200$ card will pretty much give you all the power you need for a single display at normal resolution (1920*1080) http://www.amazon.com/Eyefinity-EAH6870-DC-2DI2S-1GD5/dp/B004H8C2XO/ref=sr_1_4?s=electronics&ie=UTF8&qid=1327976039&sr=1-4 . It might chug slightly on max settings on some games. Might. It's certainly not over powered like the CPU.
RAM modules. These are really cheap. 50$ buys you more than you will need for games for a looong time. http://www.amazon.com/Kingston-Technology-Modules-KHX1600C9D3K2-8GX/dp/B0037TO5C0/ref=sr_1_2?s=electronics&ie=UTF8&qid=1327976222&sr=1-2
A good PSU will set you back though, and since a crappy one might just burn out your entire system, you don't want to skimp on this one. Good news is that a good PSU will likely outlast all your other components too, so you probably won't need to upgrade.
100$ should see you through. http://www.amazon.com/Corsair-Enthusiast-Certified-Performance-CP-9020002-NA/dp/B005E98I0G/ref=sr_1_11?s=electronics&ie=UTF8&qid=1327976369&sr=1-11 .
So that's a full gaming rig for under 700$ that will run absolutely any game out so far with no problems, on max detail. You can shave 100$ from the CPU by buying an AMD Phenom II 960T that will also run any game with no problems (this means a different, but similarly priced mobo that supports AMD processors), but is not quite as good in stuff like Photoshop, ACR, video editing, etc. You can even shave some 70$ on the video card and still get almost flawless performance in almost any game at max detail (thus bringing your rig at around 500$).
The above components would make a very nice cost/performance ratio PC, but you can look around at comparative benchmarks (tomshardware.com offers plenty of those for pretty much everything) and see what you can do with your budget.
As for pre-build rigs, well, it's all about how big a mark-up it has on it. You might be able to find great deals, all you have to do is find every component online and see how much they would cost if you'd just but the same components, but separate. Plenty of stores around here offer to assemble your PC for you and will even throw in free advice on what components to get.
I'd avoid laptops if gaming is all you are interested in. They can't match a desktop power/cost ratio.