zsara,
There are several things you need to look at.
#1 - Find out exactly which model you have (Model ID) : "Apple : About This Mac : More Info : System Report : Hardware : Model Identifier : (should be something like iMac5,1)
Note: You state Late 2006, but you say intelcore duo (if not a core 2 duo, then it's early 2006, this #1 above), depending on the model, you may only be able to get 2GB or 4GB of RAM etc. but at least it will be cheap. There are several places to purchase, I personally use Crucial, but OWC is good too.
# 2 - While using System Information (above), you could click on the "Storage" (under Hardware as well), and it would tell you how much space you've used on your Drive/s etc. You could also just highlight your Hard Drive Icon and "get info" on it (this would show you the info as well) - and as RC said above, you want at least 20GB free. Also, yes, if you need space, backup or delete any junk you don't care about (not in Apps etc.), just your own stuff.
Note: Regardless of the space left, 2006 is a blessing for you and your drive, you really should think about backing up all your stuff, and preparing for the death of the drive (I.E. replace it soon) IMHO (3 years is avg life) - Some get 1 year, some get 5 years or more, but boil it all down and you get 3 years (in my 19+ years of IT).
# 3 - As RC-R stated, open up Disk Utility and Verify, and I would also recomend running a Verify/Repair permissions (if you haven't in a long time) - This really isn't for speed, but I recomend it.
# 4 - Fragmentation (oh boy let the flame wars begin) : While in general (everyday use) OSX takes care of small file frags, it does in fact over time (especially with large files etc.) become fragmented, I'm not saying you should run out and purchase Drive Genius etc. but if you've been running this box for years on the same load of OSX, with just upgrades as you went (I.E. Never a fresh install since 2006), then you may want to think about backing up everything (Time Machine etc.) and doing a fresh install of 10.6 (via DVD). This could be done on your new drive if you choose to buy one, but if you don't, it could very well help (5% to 20% - just depends). Let the flames begin!!!
Ok it's early, and gotta run to the day job. 🙂
PS. Once you price RAM, and HDD etc. and your time spent, it may be time to peek at an upcoming Mac Mini or something. I believe in using the heck out of equipment, but that box is getting a little old in the tooth. IMHO.