Why?

CPUs progress at a pretty quick rate.  A faster CPU is one of the easiest ways to speed up your aging computer, but don't look at it as the miracle cure! If you have a lot of other slow components, the CPU's speed may not be fully realized. At any rate, installing a new CPU is easy if you are not also installing a new motherboard.

How?

1. First make sure you are getting a CPU that is compatible with your motherboard.  i.e. if you are getting a Slot 1 CPU, your motherboard better be a Slot 1 motherboard!  There are exceptions to this though - you can get a Socket 370 or FCPGA CPU and use it on a Slot 1 motherboard if you also get a Slotket adapter. 
Also make sure that your motherboard supports speeds that high speed. If the jumper settings on the motherboard itself (or the CPU settings in the BIOS) don't show settings for the newer CPU's speed, you may not be able to use it.  Check the manufacturer's website for settings for newer speed CPUs and/or for BIOS updates to support the newer CPU speeds. To check the speed capabilities in a motherboard that supports BIOS settings for the CPU speed, press F1 or Del to enter the BIOS setup when you turn your computer on (it should say Press F1 to enter setup (or something like that). 
You also need to make sure your motherboard supports the CPU's bus speed. i.e. a 133 MHz bus speed CPU will not run on a BX chipset motherboard!

2. Shutdown your computer and remove the case.  Remove the current CPU (for Socket CPUs, you need to pull a lever before the CPU can be removed; for Slot CPUs, you need to pull out on the edges of the CPU's bracket (on the left and right when looking down on the CPU from above) and lift the CPU up while you do so). Be gentle!

3. Make sure you have a properly attached heatsink and fan, then insert the new CPU into the Slot (until it snaps into the brackets) or Socket (then push down on the lever to lock it in place). 

4. Change the jumpers to match the ones in your manual for the new CPU's speed (or change the settings in the BIOS to match the CPU's speed).  Power on or restart your computer and you should be set!  No changes need to be made in the operating system (Windows, etc.).