There are places to meet characters in all of the parks at various locations in the parks. There is a set schedule for them which can be found in various places. I personally like Kenny the Pirate's site for his neat and easy to read charts.
As a general rule you should be in line 15-30 minutes in advance of the character's set meeting time (depending on how crowded the park is and how popular the characters are). They cut the lines off once they get to a set length. There's nothing worse than a child who wants to see a certain character and finding out the line is cut off all while they see other children in line meeting them... So plan, choose the ones that are "must meet", and save the others for another trip.
At MK you are able to get FP to meet Mickey/Minnie and 3 princesses (usually Cinderella, Belle, and Aurora - although they never guarantee specific characters).
At the meet and greets you can have a photo taken, have an autograph book signed and interact briefly with the character until it is the next person's turn.
Have fun!!!
ps - Yes Rapunzel has her long hair at the M&G.