This is the easiest of the three towers. This tower is pretty straight forward, but I will still tell you where the Gem is. First, climb to the top of the tower. Then, you will see a room that looks like this:
Drop down this hole, and that will bring you to the next room. It looks like this:
This is the last drop before you find the green gem. The last room will look like this:
Grab the Green Gem, and you're ready to go to the next tower. Keep in mind that it doesn't matter which tower you got to first, but it does matter what order you place the gems. You can only start placing gems after you have all three of them.