First, you will be asked to input some basic data such as Summoner Name, Region, and what team you are on (you can see this by which team has the first ban, as well as the color of the text "Your Team" above the first pick). Currently, what role you will be playing is included in this stage but will be modified - and possibly moved - to match next season's champion select.
Then, you will need to select all the bans and picks as they happen up until it is your turn. The currently banning team, or currently picking player will be highlighted. One note for this phase is that blue team is statically on the left side of this GUI, and red team is on the right, while in the client regardless of your team you will be on the left. The search bar functions the same as it does in the client. Simply click on a champion's icon to ban/pick (there is no lock in function yet, I'm debating between this and an undo button. For now, if you make a mistake you have to restart the program).