To replace the battery in an iPod 4th Gen is pretty easy and the video on this page will show you how to do it.  Many of the replacement batteries you can find here are higher capacity than the iPod came with, so your play time can be longer.  

-The original battery for the iPod 4th Gen was 600 mAhr

-Replacement batteries can be found as high as 1200 mAhr, common ones are 900 mAhr which will give you ~ 10 hrs of play time between charges, compared to the original which is ~ 7 hrs.  A 1200 mAhr battery will last ~ 11-12 hours on a charge.  It is worthwhile to check the capacity of what you are buying, because the battery price is only a few dollars more for higher capacity.

 

-The original battery for the iPod 4th Gen Color/Photo was about 680 mAhr.  The newer batteries for this model are either 900 or 1200 or 1380 mAhr, so play time is almost doubled.

 

There is a bit of ambiguity regarding the replacement batteries.  The "stock" battery for the 4th gen Mono does not work with the Photo; however, replacement batteries for the Mono/Photo (with higher capacity WILL work. 

 

The batteries to look for are compatible with 616-0183 and 616-0206; 616-0215 also appears to be compatible.

 

The 4th generation iPod range includes the following model numbers:

• M9282
• M9787
• PE435A
• M9829
• M9268
• PE436A
• M9282
• M9268
• M9830

This battery can be used to replace original-fit batteries with the following part numbers:

• 616-0183
• 616-0206
• 616-0215

 

There are some key things which will help make this successful

- During the part where you disconnect the cable on the bottom of the iPod, you should react your pulling force by holding down the part of the connector attached to the main board, if you can.  If you pull too hard, the connector can separate from the board. While this is not fatal, you will have to get a new Main Board, which will cost more than the money you saved doing this battery replacement yourself.

-Be very careful not to stress the connector which joins the board to the back plate.  If you need to remove it (to get better access to the inside of the ipod) remove the connector by prying on the hard plastic part NOT by pulling on the cable.  The cable will separate from the hard plastic part of the cable and then you will have to buy a new one.