Use two hands: Orient your card toward the recipient when presenting.
Some Japanese people are taught that a meishi is the "face" of the person giving it, so you don't want to cover theirs or your own.
You're ready to level up! Below are example sentences you can mix into your standard jikoshoukai to give it more flavor, and make your self-intro a memorable one. Act at least a little bit impressed with their job title.
When they offer their card, accept it with two hands.
Not only will Japanese be flattered, but they will be eager to know why you are studying their language. I work as a teacher. Treat meishi with respect: Use common sense and treat meishi like you would a gift.
When exchanging meishi in a group, give to the most senior person first: Start by giving your business card to the shachou, then fukushachou, and so on down the chain of command.