It's a matter of noticing when the character on the screen is getting 'light'. Don't let the battery go dead. When ready you need to get the new batteries out and having them ready right beside you and in the best grabbing position. You'll want to grab them both at the same time with one hand between your thumb and finger (or however works best for you). You undo the screw and set it aside but hold the lid on the Tama until you are ready to make the change. The batteries need the lid pressed onto the batteries on the back of the Tama for the 90's Tama's to work.
When ready you pop the lid off, turn the tama over quickly and those old batteries will drop out onto the floor/desk/whatever. Than quickly turn the Tama back up (battery side up) and quickly insert the new batteries and smack that lid into place as fast as possible. If you can do this very fast the Tama won't reset. I've done it many many times and it works out.
There's still a chance for it to reset, but at least you have a chance to save your character if those batteries aren't gonna last long enough.