When you first enter the Arena, you should enter a user name. Then, you should choose a squad of 10 Heroes - tap on one of the empty slots at the top of the screen, and you'll be prompted to add Heroes.
Once you've added 10 Heroes, tap 'DONE'. You'll see the global leaderboard, showing the top 100 PVP Players (more leaderboards will be added soon). Tap 'PLAY', and the game will search for an opponent which should be reasonably balanced with you.
Next, Drafting begins. Whoever is selected to go first chooses a leader, then their opponent does the same. Then, you choose two Heroes, and your opponent then chooses two more. This allows you to choose your Team strategically, based on the choices you see your opponent make.
Once both players have chosen their squads, the game begins.