How long will it take retainer to straighten crooked teeth?

Depends. Your result with an active retainer is dependent upon how crooked the tooth is, how much space is available to align it an d how much you wear the retainer. Full time is recommended.
Crooked teeth. First be sure that your retainer is supposed to straighten your teeth. The very term retainer means to retain which in this case is to prevent movement. There are some types of appliances that are grouped in with retainers such as a spring appliance which will move teeth but is limited. Invisalign is much like a retainer but it moves teeth. Is yours made to move teeth? Check with your doc.
Depends. Depends on how crooked your teeth are to begin with. Only orthodontist can tell you how long it will take after examining you. It will straighten up in 3 months to 1-2 years. After that, you need to still keep retainer, probably another year. It all depends on severity of crookedness.
They don't. Retainers retain, they hold things where they are. There are removable orthodontic appliances that are sometimes inappropriately called retainers, and they can affect some tooth movement. It's faster, easier, cheaper, however, to have traditional orthodontic treatment followed by one of many forms of retention to stabilize the treatment result. See a qualified orthodontic specialist for eval.
Crooked. Specific types of retainers may be used to align teeth, but the type, design, and duration of treatment is varied. In other words, the time required will be dependent upon how crowded your teeth are and how much you were the retainer. Ask your orthodontic specialist for an evaluation and estimated treatment time.