Prior to character select, each summoner is randomly placed in order 1 to 5 and one team is randomly selected to go first. (For sake of example, we'll say the blue team goes first)
On the character select screen, summoner blue 1 is up first. Summoner Blue 1 has to ban a champion. Once summoner Blue 1 bans a champ, summoner purple 1 has to select a champ. Then purple 2 must ban a champ and blue 2 must pick a champ. Blue 3 bans, purple 3 picks. Purple 4 bans, blue 4 picks. Blue 5 bans, then purple 5 picks. The 5 champs picked are now the 5 champs that both teams will use. Each team has 90 seconds to decide which player will play which champ.
Then game as normal.
Believe in yourself. Not you, that believes in me. Not me, that believes in you. Believe in you that believes in yourself. - Kamina, TTGL