Keyfob "front", index finger on the latch for the door key. As seen in this pic, push the latch to the left, then pull the door key out of the fob. Then turn the fob over.

On the back side, there is a ledge or lip just under the door key latch, as shown here, my thumb is against it. The blue arrow is pointing to the key latch, the pink arrow to the key tab that holds the key in the fob. What you can't see is that the key latch also holds the back of the fob on.

While pressing down on the key latch all the way, push the back of the fob off with your thumb. It is vital to be pushing the key latch as far as it will go, or the back will not release. Make sure not to wrap your hand around the end/top of the fob, as most of it is actually the back. It may open better when placing your thumb on the Toyota logo and pushing from there.

The back partially slid off - note the small Philips screw showing lower right.

Here is the back/top removed - note the latch mechanism is part of the back.

The back is off. Now use a very small Philips screwdriver, remove the 4 screws, remove and replace the battery (CR2032), and reverse the disassembly. Note - just as it is important to press the key latch all the way down in order to remove the back, it is necessary to press it all the way down in order to latch the back back into place.

Many stores' Jewelry counters (Walmart, Target, etc) will change the battery for you if you buy it there - just print these instructions out, or practice opening the fob before you go, and you will be out the door in minutes.  But sometimes their cost on the batteries can be high.

Dollar Tree stores often have 3-packs of CR2032 batteries up near the register on hang strips for $1.  I recommend you replace the batteries in all your fobs at the same time so you don't have to worry about when one will fail, so this 3-pack is handy.  Buy a set of jeweler's screwdrivers for $1-2, and you can change them yourself quickly and cheaply.