Trust is not like a light switch that is easily flipped back to the on position. But trust can be earned.
First, start with a sincere apology to your father. Then you may explain that you have a sincere desire to earn back his trust.
Then comes the hard part. The way to earn back that trust is by doing exactly what he asks of you. If it is an early curfew, be home five minutes early. If he asks you to do something like helping around the house, do it quickly. If he asks what you did last night, be honest and forthright. Eventually, trust is earned through honesty and punctuality.
Parents generally do not intend to ruin the lives of their children! They want what is best for you. Believe it or not, they know exactly what it is like to be a teenager! And they don't expect you to be perfect. But they do want you to be honest and cheerful. Be that person and you will end up happier. So will your parents.