All you need to do is go to the Character menu and select the Summoned character sub-menu. From there you have an entire list of the girls you've already summoned. Select the desired girl. Below her animation you can see three buttons: Bond, Promote, Upgrade.
In the Bond menu, you can see your current bonds with the girls and increased stats.
In the Promote menu, you can promote a girl once you have the required materials.
In the Upgrade menu, you can level up the girls' stats.
There's also an Evolve button near the Memory Fragments gauge you can click on to evolve the girl, to obtain a different animation of her. Remember that you need to have the required Memory Fragments to evolve a girl.
The number of hearts shows the promotion level of your girl. Promotion will increase all your stats. You need to obtain the required materials in order to promote. Take into account that characters must meet a certain level requirement before they can be promoted. You can obtain up to 3 red hearts per character.