With regards to moves. Every pokemon has only 2 moves, one 'normal' and one 'powerful'. You can do normal moves all the time by tapping, but you can only do powerful moves when the bar under your pokemon name fills up - and you do it by tapping and holding for a bit longer, until you see a message like 'Vaporeon used Aqua Tail' and then you see the action.
You can also move from side to side, this is called dodging. This way you can avoid your opponent's 'powerful' move. But this action is tricky and dodgy I guess if the game wouldn't glitch and freeze so often then perhaps you'd be able to tell better when and if your dodging actually works.