I was at a math workshop today, and from a participant I learned a great calculator skill that left me saying, "where have you been all my TI-83/4/silver edition/titanium life?".
Suppose you're graphing, and suppose you simultaneously want to see the graph and the table screens. Well: mode > G-T, and poof, when you hit graph, voila, split screen. Then you can toggle between the 2 parts by hitting the "table" or "graph" button, and then you can do whatever you want on that part of the screen.
Also, you can split the screen horizontally (mode > horiz ...) and then you can show the graph and either the main window or the lists or a table, etc.