After choosing your move and or item and clicking the attack button both the opponent pokemon and your Pokemom get to attack at the same time. Then the messages appear below your Pokemon explaining what the respective Pokemon did last turn. After attack the percentage will go down and if the opponents percentage reaches zero, the opponents Pokemon will faint and will automatically bring out their next Pokemom (As shown in the screenshot). If your Pokemom faints u have the option to chose which Pokemon you want to bring out. Battling does not require a page refresh.
//Sorry if any spelling or grammar mistakes, sent this on my phone