Hi there!
If you're saying that the fan is weak (maybe it only works on high or low, and is very weak on any other setting...or is weak on all settings) there is a good chance it is your "HVAC Blower Motor Resistor". This was the case on my 99 Cavalier a couple years ago.
This part is prone to corrosion and melting. It is the bridge piece between the power to your fan, and the fan itself. This resistor basically gives you the ability to make your fan on your A/C or heat blow at variable speeds. (i.e. if the power supply went directly to your fan without this piece, it would only give you two speeds: on or off. This part lets you "resist" how much power is being given to your fan and put it on High, Med High, Med Low, or Low.)
I am actually a car repair novice, but I've done a LOT of self instruction on this particular car (99 Cavalier) because it's an excellent model, and has not given me too many problems. I have done a lot of minor work on it myself, including this part.
The HVAC Blower Motor Resistor (found here, also available other places:
http://goo.gl/GHDZCx) is accessible and easily changed even for a novice and if you have some time and are fairly nimble (I'll explain this in a minute), you can get this changed really cheaply. The part is about $20 and took me about two hours (with no help like I'm giving you, so maybe shorter for you).
The trick is it's location: it's tucked up behind the glove box right above the kick panel on the passenger side. If you go to the passenger side and remove the carpeting from up behind the glove box, peel it down, and peer up behind the glove box, it will be up there (I forget if there are any doors or panels in the way, but if so, they are easily removed. Just keep track of what screws come from where).
The "being nimble" part I mentioned before was because the passenger seat didn't go back far enough for me to squat and get a good look in there, so I eventually found myself "sitting" upside-down on the passenger seat, on my back, with my head tucked up near where the part is located (where your feet normally go) and my feet up near the headrest (putting the seat reclined all the way back to make it as flat as possible).
Maybe there's a better way to position yourself in the cabin to reach this part, but I couldn't find it. You'll need a ratchet set, a screw driver, maybe a knife to clear the carpeting back, and some time and patience. (Forgive me if you discover you need another tool...this was over three years ago that I changed this!) This type of twisting-ratchet tool was lent to me at the time, and it was WAY easier than a traditional ratchet handle, considering how hard the part was to reach:
http://amzn.com/B000HEKV1W . I couldn't swing a traditional ratchet wrench back and forth, so this twist-style was a life saver!
This part, once unscrewed from its harness, pops out, can easily be swapped for the new one, and as long as you kept track of your parts (not too many in the way for this repair), you'll be back together very quickly!
I hope this helps, and that this is in fact the part you need to change.