I dont actually own a cycling helmet, but I'm thinking its probably a good idea to get one!
I want to buy one from the internet (mainly because its cheaper than stores), but what do I need to look for? How do I know which is the correct size?
In the US you need to look for one of three certifications:
It's likely that helmets available online and for the UK market will carry one of the US certifications as well as a similar EU certification. I know there is a "CE" certification but I don't know about what it entails.
Any helmet meeting one of those certifications will provide the basic level of protection you are looking for, even if it is just $15-$20 US. Beyond that comes the world of look, style and performance. As helmets increase in price, they decrease in weight, increase in vents, and sometimes increase in adjustability.
I know you mention that you want to buy online, but you may want to purchase your first one at your local shop for the following reasons.
After the first helmet you will have a better idea of what you like and what fits, and you can shop around online. You will want to replace your helmet every couple of years anyway, as it loses structural integrity overtime.
In Britain the current standard for helmets is BS EN 1078:1997
Helmets for pedal cyclists and for users of skateboards and roller skates. Standards aside though, in general what you want in a helmet is something that feels comfortable, that once properly done up doesn't "slosh" around your head, one that doesn't restrict your vision and has enough ventilation to stop your head from getting too hot.
"Nice to haves" are a pleasant design and the ability to add a peak (visor) for summer riding (to keep the sun off your face).
Oh, and if you ever ride in Australia in the springtime somewhere to put some magpie deterrents.