What my colleagues are trying to say is that there are several factors to consider in upgrading your iMac. Your machine is CAPABLE of running the very latest release, OS X Mountain Lion (10.8). But there are several steps involved to avoid problems. Let's go over them.
1. How much free space have you got left on your hard drive? Is it time to get a larger-capacity one?
2. How good have you been about keeping your software up-to-date? Not just the OS, I mean all the apps.
3. How much RAM do you have on that machine? If you can be more specific about what model it is we can tell you how much it can hold maximum. I'd recommend for an old machine like that to bump it up to the max.
As for how to upgrade the OS, as harryb hinted you'll have to get Snow Leopard first, and the only way to do that now is to call Apple and order a copy. Happily, it's cheap: $30.
Once you upgrade to Snow Leopard, you'll need to update many of your apps and of course run Software Update in order to bring your OS up to the last version of Snow Leopard, 10.6.8. Everything needs to be updated together, so use a free app like Bodega or AppFresh to find out if your third-party apps can also be updated. Be prepared for the fact that some software may have been discontinued and/or can't be updated, like AppleWorks. If you have documents in outdated formats, let us know and we can advise you from there. AppleWorks continues to function in Snow Leopard but it is long obsolete now and you won't be able to move forward with AppleWorks documents going to Mountain Lion, so it's best to convert them BEFORE you get caught up a creek.
So, once you're on Snow Leopard 10.6.8 you'll have the Mac App Store, from which you can order Mountain Lion (you'll be skipping Lion) using your Apple ID. Again: your old PowerPC only apps WILL NOT WORK and must be upgraded or replaced. I have to point out that you could have mitigated this quite extensively by keeping up with system OS and app updates over the past four plus years.
You'll be gaining a LOT of new features, so take the time to learn them. You'll also be gaining iCloud, a huge benefit particularly if you use any iOS devices like iPhones and iPads.
This is a big jump you are making; don't leap unprepared.