Upgrade a very out of date Mac?

I'm trying to download a work file and also update my iphone 5 but it seems I have never upgraded my desktop mac. Its still using 10.5.8. I understand I need to go up the stages with the upgrades but how?
It also states I have only 1gb… Thats not alot right? So how do I make that bigger?

I have tried downloading Snow Leopard 10.6 but it didn't work so I have now bought the installation dvd… Can anyone give me any advise on how to get this computer back up to date.
I'm really not confident using mac at all so a /dummy. Guide' would be helpful.

If you have an older Mac, it's impossible to upgrade your iTunes and get certain downloads. I have this problem. I have a Mac G5 and I can't upgrade iTunes, so I just listen to the music from the computer as if it were an iPod, haha. But yeah you're gonna have to get a new computer if you want to upgrade to the latest iTunes software.

OS X: Updating OS X and Mac App Store apps http://support.apple.com/.../kb/HT1338

How to Upgrade My iMac http://www.ehow.com/...-imac.html

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