Bicycle Mechanics - Bike Chain

I am looking to replace the chain on my bike which i have never done before. I am looking for the correct chain and see that there are chains maked with different speeds like 7 and 8. What is the difference between these and may i need a specific one? Also does anyone have any tips when replacing the chain?

Width is the difference. If you use a lower speed chain with a drive train that has a higher number of speeds, the chain will stick against adjacent sprockets in the cassette. If you use higher speed chain on a lower speed drive, the sprockets can be too thick to fit inside the chain.

There is some overlap in what's acceptable to use. What sort of drivetrain do you have?

I am new to all of these terms and just decided to pull my bike out of maintanence. I figured it would need a little maintenance and the chain would need replaced. All i can say is that i know it is 21 speed, but i haven't even taken it our yet. I am pretty sure the gears are 3 on one side and 7 on the other making 21. Can you tell what i would need from that?

If that's a 7 speed freewheel, you need a 7 speed chain. I use a SRAM PC-870 on my 7 speed.

The chain needs replacing when it skips a few teeth when you pedal hard. If that's not happening, then clean it, lube it, and use it.

If that's a 7 speed freewheel, you need a 7 speed chain. I use a SRAM PC-870 on my 7 speed.

?
A seven speed can be either a freewheel or a cassette.
To know if you need a cassette you need to measure the chain. When any one foot interval of chain becomes elongated to 12 1/16th inches if needs to be replaced. Use a good steel ruler with all of the slack out of the chain. If a chain is allowed to stretch more than 1/16" per foot the cogs may be worn enough that the new chain will skip on the teeth.
A 7-speed or 8-speed chain will work.

If that's a 7 speed freewheel, you need a 7 speed chain. I use a SRAM PC-870 on my 7 speed.

Not quite 100% accurate. 7-speed will fit with chains marked "6,7,8" on them.

I have an old 6 speed bike (6 cogs on the freewheel in back, 2 chainrings on the front, used to be called 12 speed), and I was able to replace the old chain with a new 8 speed chain. The only problem is that once I did that, the new chain would skip on the old cogs in back due to the mismatch of having a new chain running with the old worn cog teeth. Then I had to replace the old freewheel with a new one (only $15). Since my old chain didn't really have visible corrosion, I probably could've saved the money and just rode it until it started skipping on its own/started to rust/exploded. On the plus side, I now have a really shiny new freewheel and well-lubed new chain...

One tip not mentioned, don't assume that the chain you had on previously was the right length. The one I had was actually one link too long. There are a number of ways people determine the right length, I used 3 outta the 4 listed in Leonard Zinn's book and that's how I found out my old chain was too long.

The Park Tool how-to's are awesome:
http://www.parktool.com/repair/byregion.asp?catid=5