When you rise, the action is more of a pevlic tilt than literally lifting yourself out of the saddle. That is a very common mistake that beginners will make, thinking that you have to go up and down by pushing yourself out of the saddle.
It really doesn't need to be that hard ;) Don't grip your knee as it will make your lower leg swing back, instead hold with your calf muscles. Eventually when you develop an independant seat, you will have no gripping/tightness in your joints when rising.
Think of rising as though you are pushing your pelvis towards your hands. You only want to come out of the saddle slightly, so there is just a little bit of under under your seat. Let your horse 'bump' you out of the saddle just enough to push your pelvis towards your hands, don't force the issue, you will see what I mean when you ride ;) Also when you sit, THAT is when you want to put your leg on, as that is when the inside hind leg is leaving the ground and thus the time in which you have the most influence over it.
For sit trot, there are lots of good posts on this forum about how to sit trot. Under horse riding, english riding and dressage.