I have a laptop (not suitable for games) but in my house there's this 5-ish year old desktop which i want to convert into a gaming rig.

The desktop is a Dell Dimension 8400-> http://reviews.cnet.co.uk/desktops/0,39029979,39188932,00.htm

What are the steps required to do improve it and what hardware would you recommend??

Thanks for helping this newbie.For most gaming upgrades, you usually want to upgrade the RAM, and Graphics Card.

I'm not an expert at the gaming upgrades, but seems to be that your Processor is fine(3 GHz).

Add about another stick of RAM(2GB Stick). And get a GFX card that has atleast 128MB of VRAMYou'll have trouble upgrading a Dell's graphics card due to the power supply.
What sort of games are you looking to play, and what's your budget?He may also need to get another power Molex SPLITTER if he needs a DVD drive for some newer gamesMy budget is around $300 but can be adjusted up or HOPEFULLY down.

and the games i would play would be mostly in the first person shooter genre, specifically games like call of duty and mass effect.

ThanksI'm finding conflicting information about your power supply options.
Some information suggests it's just STANDARD ATX and can be REPLACED with any normal PSU ... some says a normal PSU won't fit in the case ... some say there are some weird connectors that aren't on a standard PSU, which may or may not be needed.
The most COMPATIBLE option would be a Dell-compatible unit from PC Power & Cooling, but that's very expensive for what it is.
I'll keep looking.