*Get some needle-nose pliers or tweezers to unscrew the single metal screw on the cart, this is the hardest part of the whole process.
*Open the cart, the older GBC games actually slide open but I can't remember if GBA games do the same or not. Now the second hardest part, getting the old battery out. You need to unattach the two metal tabs on either side of the battery without damaging them too badly. I used an exacto knife to peel the tabs off. You can use your pliers (assuming they don't have teeth) to flatten the tabs back out afterward.
*Now that you have taken the old battery out, you can run down to your local Walgreens or whatever and get one of the same kind, refer to the number on the battery, it will be something like cr2032, 2025... those are just examples. Just get the same thing as on the battery.
*Now put your new battery on the bottom tab make sure you have the negative and positives aligned correctly and tape the bottom tab (-) to the bottom of the battery, you will have to bend the tab slightly to do this. Now push the battery in place and tape the top tab (+) to the top of the battery. Now you need to make sure the battery stays in place, so you need to place something between the cart and the battery to keep it snug. So slide either some paper, carboard or keep adding layers of tape until the cart has a ever so slight buldge were the battery is, this helps make sure it won't come out of place. I've even heard of people wrapping tape around the whole board and the battery but I don't recommend this...
*Screw the single screw down tight again, and turn on your game and hope for the best. I had to do this whole process twice for my silver because the first time I didn't have enough pressure in between the battery and cart, so don't skimp out on that.