What should I bid after my opponent has opened the bidding?

I assume your opponent opened 1♣

I would double with your hand.  “As an Overcaller all really good hands start with a double.”

After the double, your partner should cuebid the opponent’s suit by bidding 2♣.  This is a common practice used to show  a hand holding 12+ HCP, that isn’t sure either where to play or at what level.  You’ll bid 3♥, showing long hearts, setting hearts as trumps and a hand that was too strong to simply overcall.  3♥, in this context, is a game forcing bid.  Things get a little difficult at this point if you’re not familiar with more advanced concepts that established partnerships usually agree and discuss.

What should happen is that your partner will cuebid the ♠A and you will probably just bid 6♥

There is a bid that could be used to explore seven, called Exclusion Blackwood…..but that’s something that only high level players employ.  Even they sometimes have problems with these auctions.