Tamagotchi batteries are similar to watch batteries. They cost £1-£3 if you buy them from shops and sometimes you can buy 20 batteries for £5 on websites like ebay.
Downloading is when you change your tamas battery then press the "reset" button at the back of your tama, then press button "B"
and select download. If you downlaod it, your tama will go back to where you last left it.