When a battle starts, you have 20 seconds to choose the first Minions to be called on the field. You have 60 points to spend for this phase. Use the Minions hotbar to do so. Above it, you'll see the cost gauge filling as you make your choices.
Every Minions called in the Briefing phase will now appear on the battlefield and the fight begins.
From now on, you have 240 cost points to spend. When you call a Minion, it's placed in the summoning queue until its appearance on the field. The cost gauge is filled with green for Minions already on the field, and with orange for those in the queue. Even when the gauge is filled, you can still have up to 3 more Minions in the summoning queue.