Instructions
Play through the game's story mode until you complete your first tag team duel against Leo and Luna with Blister as your partner. This serves as a tutorial for how tag team duels work. After beating Leo and Luna, you will have to find a tag team partner to replace Blister.
Return to any person you've already dueled. Pick any character whose deck impressed you. Any partner you pick will ultimately not be that helpful in beating your opponents, so go for someone that has powerful cards.
Speak with the person you want to partner up with and challenge him to a duel. Keep battling him and win each duel until he asks if you want him as a tag team partner. Agree and he will join you for tag team duels. If you decide you want someone else as a partner, duel him until he asks the same question -- if you agree to partner up with him, he will replace your current partner.