Here should come up some help for new players. This could contain how to fight in the best way.
To dodge easily swipe left or right right after the screen flashes yellow. You'll have time for 1-2 attacks right after dodge.
Do keep in mind, that opponent attacks 2 times in a row, when a new battle starts.
There are 2 different types of attacks on every Pokemon that are picked from a pool of attacks for that specific pokemon. Evolving the pokemon chooses new attacks randomly.
For the Basic attack just tap on screen. This is your default attack.
When the fight lasts long enough the blue bar below the health-bar fills up. (needed for attack number 2)
Attack 2: For the special attacks you need to fill up the blue power bar below the health bar by dealing damage to the opponents Pokemon. You can use the special attack when the power bar fills up by long pressing on the screen. Some pokemons can save up enough power for multiple special attacks.