Vocal instructors charge anywhere from $20 - $240 /hr
Like most things, you get what you pay for; buy cheap, you get cheap.
Here in L.A, the average is around $60-$100 for decent lessons and $120 - $240 /hr for premiere instruction.
In large metropolitan areas, you will have a wide variety to choose from and
in small towns only a few if any.
A good instructor will coach you up, record to CD your session, and you should
leave after the first session with marked improvement and homework.
When choosing an instructor, ask for resume, past students and if you can possibly get
an introductory lesson. Also, see if they have anything online.
Obviously, if you are not impressed with their vocal technique, why would you pay to learn that?
From having observed numerous vocal instruction sessions, (BTW, I am not a singer nor claim to be one)
They usually will work on your "mix" the transition from chest to head voice, have you land on notes rather than sliding up to to the note, breathing, posture and vocal-ese; warm up exercises.
Good Luck and with practice you'll not have to worry about having your studio vocal tracks completely autotuned.