It will not be instant. Sit down with them and tell them that you realize that some of your past actions led to their not trusting you (shows maturity). Tell them you appreciate the actions that they took at that time, and you understand why they became more restrictive of your activities.
Tell them that you have changed (give concrete examples like “I know I was hanging out with the wrong crowd. I have made new friends.” or “I know it was a mistake to smoke dope, and I am not doing it ever again.” or whatever.).
Tell them that you would like an opportunity to regain their trust. Tell them you realize that it will take time. Ask them what small steps you and they might take together to make that happen. Ask, for example, if your curfew could move from 11 P.M. to 11:30 P.M. or ask if, since you have brought your grades up, you be allowed to go out both Friday and Saturday nights. Start by only asking for one change.
The stick to whatever you agree to with them for a while. If your curfew is loosened a little, make darn sure you are home by then. If they give you an extra night to go out, avoid the inquisition by offering to tell them where you are going, who you will be with, and when you will be home.
You get trust by being trustworthy. If this first step works, meet again with them in a month, and negotiate another loosening of the reins.