From your experience how long does a wrist sprain take to get better and heal?

Depends. Most strains in the wrist tend to improve and resolve over a 4-6 week period. A sprain (defined as a tear) in the wrist where a ligament has torn don't tend to do so well. Most ligament tears in and around the wrist result in some degree of permanent disability. Some can be improved with surgery, but many can not.