Go to the Apple Menu in the Menu Bar/Software Update. Run Software Update to see the available updates. Depending on what problems you're having, one or more of the updates may help.
If you have an early 2008 iMac(8,1) you most likely have Leopard 10.5... To upgrade to Lion or Mountain lion you will need to purchase Snow leopard 10.6 and then update the OS to 10.6.8 either via Software Update or downloading the 10.6.8 Combo Update directly from Apple's download page.
I have a friend with an early 2008 iMac that has 1 GB of RAM. I would upgrade your RAM to 4 GB if you plan on doing any OS updates.
Start by checking if you can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
Whilst Apple have withdrawn Snow Leopard from their stores, you can still get it from Apple by calling 1-800-MY-APPLE (if you are in the USA) and they will supply the SL DVD for $20 for a single user, or $30 for a family pack that covers up to 5 Macs. You can also purchase the code to use to download Lion from the same number (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:
If you are outside the US call your national Apple Helpline:
If you're in the UK, use this number: 0871 508 4400
When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.
To use iCloud you have to upgrade all the way to Mountain Lion: