1-on-1 situations can happen as a result of a team's error, a pass interception or a breakaway. Usually, the only obstacle between the offensive player scoring after overcoming a 1-on-1 is the goalie.
If your coach chooses to play 1-on-1, be sure that your team is giving constant pressure. Pressure is what will force the other team to move the ball, and will hopefully result in a turnover.
Many offensive players will try to fake out the defender, because as soon as the offensive player gains the advantage, there's nothing stopping him from taking a shot on goal. Being quick on your feet is going to allow you to keep your opponent in front of you and away from the goal.
If your opponents are putting 1-on-1 on your team, keep your touches tight. This is extremely important to maintain control. Failure to bounce back on quick turnovers can make or break you gaining the advantage on 1-on-1.