I started new birth control, how long does it take to be effective?

Next cycle/depend. Once you start on bcp for sure after your first month, it is effective.I always tell my pt to use extra protection with foam and condom the first month when you start bcp.However, if you are already on the pills and your doctor change to a different one, then you do not need extra protection.As long as you take regularly and not skipping anyday.
Depends. Depends on what type of birth control. Read the package insert (if you threw it away, look up the brand name and "package insert"). Please consider using barrier contraception too - often stds do not cause any symptoms at all, at least initially. Your partner may not know if they have an infection. Be safe.