Three 1* cards of the same "suite" (aka identical in species AND variety, there are several cards with the same species but different color patterns) should automatically combine into one 2* card in your hand, and then three 2* cards should become one 3* card.
As @Reave said you need 3 of the same card to combine it. But there was a glitch with some of them where they just wouldn't combine even with the 3 and never heard if they fixed that or not