Replacing batteries in an iPod has significantly different degrees of difficulty depending on which iPod you have.

 

iPod Nano:

The Nano has batteries which are soldered onto the main board.  This makes it more difficult and you will have to be quite good at soldering to do it.  And even if you are quite good at soldering, the terminals are SO small (as small as the head of a pin or smaller) that replacement is very difficult.

The exception is the 1st generation:  it too is soldered in, but you can cut the wires long, and attach a new battery by using crimp beads or by soldering.  You will then need to cover the joint with electrical tape (Kapton is preferred) in order for it not to short to the rest of the circuitry.

Additionally, the Nano 3rd gen has a back cover which is very difficult to remove without bending it permanently.

 

NANO Battery Replacement:  Best left to professionals.

 

Ipod Battery Replacement:

For the iPod, the batteries have a small jack type of connector on the end which makes their replacement easy.  The most difficult part of this process is opening the iPod.

 

You will need to find the correct battery for your iPod.  They are in general not interchangeable.  The video iPods (gen 5 and 6) are much higher capacity than previous generations.