There are currently only two gamemodes, Objective Control and Power Collection. You can't choose which one to play, so when you search for a match, you get into either, randomly.
During the collection phase, break and take as many cells as possible - you can see their locations on the map. By killing enemies, you can take the cells they were holding at the time. Once all cells are collected, the hand in phase begins.
Try to be careful, avoid enemies, if multiple hand in points are available, try to take the longer route around and deposit them there. You must stay on the point without moving, dealing or taking damage for a few seconds to hand them in.
A little side note: if for example your team only needs 1 cell left to win (score is 49) and you hand in 10, you will only get credit for 1.