How did the conflict get resolved (if it was resolved)?

To some extent, the question should clarify which conflict is resolved (or not resolved). If we are talking about the person versus person conflict that involves Katniss having to survive against other teenagers that are trying to kill her, then yes, that conflict gets resolved. Katniss and Peeta find a way to both survive, and all of the other combatants are dead. Katniss gets to return home.  
However, The Hunger Games is book one of a trilogy, so some conflicts are left open. Katniss's struggle with exactly how to deal with her feelings for Peeta and Gail are not resolved. She knows that she doesn't love Peeta the way that she acted to in the Hunger Games, but she knows that the act must be kept up for both of their sakes. The other conflict that doesn't get resolved by the end of book one is the conflict that most of the districts have with the Capitol. The Capitol retains its power over the other districts, and the Hunger Games themselves are going to continue to happen. Katniss has inspired some credible dissent against the Capitol from other districts, but that conflict is only just beginning by the end of the first book.