There are two methods to summon new characters in the game. A Single Summon uses 5 Dragon Stones for a chance to get a R character minimum up to a SSR. A Multi-Summon requires 50 Dragon Stones which will give you 10 characters PLUS a guaranteed SR character. The latter option is the bang for the buck since a Guaranteed SR is already a bonus and you have 10 chances of getting a SSR character. The SSR characters available for "pulling" changes over time. Check the Scouter in the Summon menu to learn about the available characters you can potentially get when summoning.
You can also perform a Friend Summon. This utilizes Friend Points to summon. A single summon costs 200 Friend Points and a Multi-Summon costs 2000 FP. Unlike the premium summon, there's no guaranteed card as a bonus for multi-summon. Also, the highest rarity you can get from this method is R and you'll most likely get fodder most of the time. However, since there are no other uses for FP in the game aside from this, don't hesitate to spend them to get normal characters that you can use to "feed" your main cards for Training.