Hi Susan ;)
From one Sansa Clip enthusiast to another, I hope this helps!
How to replace a Sansa Clip internal battery.
1. To open the case you'll need a plastic prying tool.
2. You'll need a pencil-style soldering iron.
3. 25-watt for general circuit board work, I use one that switches from 15 to 30-watt. Radio Shack sells several models for under $20.
NOTE: When soldering electronics with irons greater than 15 Watts, minimize extended contact with the board (more than 5 seconds at a time) as it can cause damage. Also, after soldering a point, let the solder cool for 3-5 seconds before wiggling any wires and etc. as it's still molten and they'll shift out of place if it hasn't hardened.
4 & 5. An example of the tools and the battery which is a replacement for an ipod shuffle.
The old battery has an attached small board which is connected to the player via 3 wires. This board has to be reused, so rather than removing the wires, you have to remove the board from the battery. This also means you have to take care not to damage the board.
To do this, desolder the points on either end of the small board where two silver ribbons from the end of the battery cell are connected, don't worry about the condition of these since they're part of the battery and will be discarded. Also, notice on the battery surface it shows + on the left and - on the right, FYI.
After that, you will have to do the same on the new battery, since the Shuffle circuit is not compatible. Same procedure, two points on either end of the small board attached to the battery cell, however take care to keep the silver ribbons as intact as possible, the board can be damaged since it will be discarded. The poles are the same, and similarly labelled with a + on the left, and a - on the right.
Note: Many times batteries come with a plastic label stuck to the outside of it, this can be easily peeled off to reveal the attached board and + - markings on the battery casing, just be careful not to damage connections from battery to board.
Last, you might have guessed, solder the new cell to the board which the old battery was removed from. Once soldered, you can clean it up a bit with some rubbing alcohol and Q-Tips if it looks gooey. Cover the board connections and battery end with one or two wraps of electrical tape. Don't overdo it so it's not too thick. Lay the battery in it's new home! Adding a piece of 2-sided tape or such to hold it in place is optional but probably not needed.
Reassemble, taking care to seat the power and volume buttons into place BEFORE you forget and have to pry it apart again.
6. Standard electronics silver-bearing solder, 62/36/2, I would use .022 or .015 diameter wire, you won't need much though. Might pick up some copper desoldering wick also (all sold at Radio Shack) for removing excess. Can be a lifesaver.
7. Replacement for iPod Shuffle battery 616-0212 (the original iPod part number) is what you'll need to know, since there are lots of after market battery manufacturers to choose from. The original Clip battery is 3.7V 300mAh, so make sure to get the shuffle battery that is 300mAh since they also sell a 250mAh. They both would work, the 250 won't provide as much playtime per charge though.
That's it! New battery should have around half a charge, which you can use, or charge as you usually would, and go!