What is this plant? How do I trim it?

We have been busy the last few weeks trying to clean and organize the house now that marching band season is over and we have time again. Walls have been painted and now the wooden floors are getting a coat of polyurethane (but we need to stop until January to make room for the Christmas tree).

So, my two remaining indoor plants received some tender loving care.
The table they sit on has a new coat of polyurethane.

This plant is a gift from my good friend when my Dad passed away.

It has gotten so big that when on its table, it reaches the ceiling!

I am not sure what kind of plant it is and I am not sure how I can trim it down. It grows on three stalks out the top.

Here it is after getting a shower in the bathroom to take off all the dust and drench it with a good drink of water. Yes, it's as wide as my bathroom!

Here it is moved to my kitchen table (because what else do I do when I cannot sleep at 5 a.m. in the morning but take photos?) There is no room left on my poor table! I had to stick a stake in it to keep the one branch from falling over.

I hardly ever water these poor plants, so I really do not understand how they are thriving and growing.

I sprayed this Green Glo stuff all over the leaves to make the plant look pretty again.The leaves are all now oh, so shiny again! I wish I could do this to my hair to make it shiny, pretty, and perfect again!

Here is the other indoor plant. The scouts gave it to me with my grandparents died two weeks apart from each other, so it also has a special meaning for me. This plant also got a bath and shining up. It also got trimmed up and staked down as it was growing everywhere.

I put the cuttings in a bowl of water and do hope they grow roots. I will have to be on the lookout for a nice pot to plant them in.