I'm choosing components for a new computer I want to build, but how am I supposed to know if the parts are compatable with other parts? Also, other than the obvious components, is there anything else I'll need like screws?
The case usually comes with all the screws you need.
You will need some thermal compound. I recommend Arctic Silver 5. Some heatsinks come with a small tube of thermal compound; I recommend throwing that stuff away.
As for compatibility, there are a few things to look for:
Ram: Make sure to get the right DDR (DDR2 or DDR3), speeds also matter, but slow ram should work without issue (other than the issue of being a bit slower).
They are selling new intel mainboards with three different socket types, and AMD boards with two different socket types. If you can get an board with an 1156 socket, and a quad core intel i5, this would probably be a good combination.
Video cards are still available on three flavors...onboard (built into the mainboard, so no compatibility issues to worry about), AGP (old style; only old mainboards support this, and only old video chips are available on these cards, and PCIe x16 or PCI express x16 (same thing)...this is the latest form...most new mainboards have at least one of these slots, and some have lots of these slots. The only other thing to know about video card compatibility has to do with power; newer video cards can use lots of power, and can thus overload weaker power supplies.