Trees are one of the most annoying terrain features to store. In order to get them to stand, you have to have a decent base size for them. I've been trying different ways to be able to remove them from the base, but still keep them sturdy on the table. Simply pushing them into the base usually works fine for a while, but the edges of the hole wear out and then the trees start leaning this way and that. Using the bases they sometimes come with (like the train model trees that you can push into a tiny stump) is also not particularly sturdy and trees will still lean and fall over.
Last night I finalized my method. Using the plastic train model trees (as well as some home made ones), I drill out the center and insert a threaded 6/32 rod. Then, using a foam sculpting tool, I push a hole through the foam base. I widen the whole on the underside and then put a washer and nut on the threaded rod. I tighten it up with a socket attachment on a screwdriver and tighten until the tree is sturdy.
It takes a few more minutes to prepare for a game, but is well worth it. I probably would not want to do it with a score or more trees, but for the 2'x2' boards I use, it works perfectly.