Stretch out the cord and look for snags or tangles. Untie any knots that shouldn't be there and straighten out the cord as much as possible so it moves smoothly again.
Tie two parts of a broken cord together in a knot to repair the break if that section of cord doesn't go through the blinds themselves. A thick knot gets stuck if it is too high on the cord, but this method woks well on the pull portion of the cord if it's low enough.
Apply epoxy glue to both parts of a cord break that have to thread through the blind's brackets. Wrap a soft cloth around the two ends and press them tightly together until the epoxy fully dries. Rub off any excess with fine sandpaper once it's dried to smooth out the repair.
Restring the blinds with a new cord if the blinds still aren't working properly. Follow the instructions for your specific blind set in this case, because the method varies depending on the set.