If you have clinical depression, Prozac is an effective anti-depressant (it's also used to treat some other disorders, such as OCD and anxiety disorders).
But (like most medications) it doesn't work for everyone, and some people find that the side-effects they experience - such as headaches or jitteriness - are too severe for them to continue taking the medication.
It may take several weeks for both the benefits and side-effects to "kick in", so don't expect instant results. If there are problems, you may need to talk to your doctor about changing the dosage or trying different medication, or coming off medication altogether.
And it's an anti-depressant, not a "happy drug": it can prevent you from being depressed, but it can't make you happy or stop you from feeling sadness.
(Personally, I've proved on many occasions that it's possible to be a cynical, grumpy, and sometimes downright miserable person while on Prozac).
If your depression is partly or entirely due to stresses and emotional problems in your life (rather than originating in your brain chemistry), it's important to remember that Prozac can't fix those (although it may act as a "safety net" to help you take action to deal with those problems).
If what you need is counselling or therapy, Prozac can't subsitute for that.
And even with depression or anxiety that's purely chemical in origin, there are lots of things that can help in addition to medication, from meditation and yoga to cognitive-behavioural therapy.
So personally, I'd have to say it bothers me when some doctors seem to adopt the "you're depressed, here's a prescription, go away" approach.
Some other threads about Prozac and related drugs: