Psychologists' rates typically start at about $100 per clinical hour (i.e., 50 minutes) and up. The initial assessment is usually more expensive than a routine session and lasts a bit longer (around an hour and a half).
If you have insurance, you typically are responsible only for a co-pay.
 In answer to your supplementary question: absolutely yes. Scientific evidence has been mounting for many years which suggests that psychotherapy does, indeed, make a major, measurable, positive difference. Some conditions, of course, require medication. Others may require only HIGH QUALITY psychotherapy. Many conditions respond best to a combination of both medication and psychotherapy.
The key is to find the right therapist FOR YOU. This may not happen the first time around. Like any other field, there are excellent therapists, and there are poor ones. Hopefully, you'll find someone highly qualified with whom you "click" right away.
If you do not find that person straight away - do NOT give up.
Therapy can have some amazing results.