To summon more heroes you will need either Trinity Vouchers or Friendship Vouchers, both of which need to be earned. This can be done by clicking on the 'Mission' tab and completing the the various Daily Quests, Challenges, and Feats which will all reward plenty of vouchers, EXP and gear.
The other way vouchers can be earned is by rewards in the 'Events' tab. The events on offer will depend on when you're logging in. At the time of writing there are four different events available and each will also give you a variety of rewards that will help you power up and summon new heroes.
Another way to get Trinity Vouchers and Friendship Vouchers is through the Path of Light quests which can be found underneath your character portrait on the world screen. There will be seven days worth of quests and completing many of them will reward you with the vouchers you need for summoning.