What is the cause and fix to water slowly coming out of an outdoor faucet when its turned off?
Oops, I think I misunderstood the question.

It sounds like this is a "frostproof" spigot.  If so, there should be a small white plastic cap on the top of the spigot just behind the knob.  A picture would ensure that a proper identification is made.

Most of these spigots can be rebuilt.  However, it may be more efficient (time wise) to replace it (depending on brand, age, availability of suitable parts).  But... this depends on how accessible the body of the valve is in your structure.  Again, a picture is going to help a lot.