It depends on your level, but you can pretty much always perform somewhere if you want to.
There are more ideas on the site. Churches, retirement homes... They won't say no.
Grab someone and have them listen to you. I did that a few times -- Just stop someone and ask if they will listen to you play a piece. Have performance parties with your friends.
"Make" the opportunities happen I guess. After some people know you're musical, they will ask you to play for things. Weddings, receptions, etc. Weddings are going to cut it for a concert career though. You need to win competitions.
And then "make" people know of you. Advertise. Promote yourself. If you give a recital, give a press release to the newspapers -- They might print a paragraph blurb about your recital. It's even easier now with internet -- You can email a press release in. Take a picture of the performance and send that in afterward. Write the story for them. Copy the format and style of other recital articles. Make it easy for them. If it's a more prestigous newspaper, ask a reviewer to come out -- Have them make an official comment and then you've got that forever, for an article... for your press kit, "So-and-so from X-newspaper said mycrabface plays piano like a pianist!"

Pair up with somebody. Play duets. Get someone whose slightly above you for being known. I see a few pop stars doing that now too. You can "borrow" part of someone else's audience.
Colleges, churches... You can do recitals there. Then promote it yourself through the newspaper.
Start small. Start somewhere. You'd have to wow your teacher and wow everyone with some local competitions. Then move up. Bigger schools, better teacher, bigger competitions. Win an international competition that includes a CD and orchestra performance and an agent. If you're that good, a wedding performance means practically squat though.
Your teacher can help find competitions. If not, ask at college and universities and groups like MTNA, Music Teachers National Association.