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