TBH, if you don't know the share market this isn't really the time to get started. You might be lucky and buy shares that are just undervalued because the market's down or you might buy shares in a company that is about to under and loose it all.
I have RBS shares, banks used to be considered safe, unexciting shares and yet they're about to be nationalised. It's just much to unpredictable at the moment unless you are prepared to loose all the money.
That said, there are lots of online stockbrokers, I can't remember who we use. Try checking out some of the financial advice websites to see if they have recommendations.
If you're prepared to lose it all then by all means do it as a gamble. Over the long term shares should come back up - as a whole, in general, could be a few that sink without trace along the way etc.
Look at online share dealing services & make sure you know how much they'll charge you to buy and to sell the shares, as the shares will need to rise by more than that if you are to make any profit at all.
You could look at a unit trust where your money is pooled together with other people's and a fund manager makes the investments for you with the aim to maximise the return. Probably worth considering if you don't want to spend a lot of time researching and playing with your shares.
I think it's probably still a bit early to be thinking about investing as the stock market may still have a way to fall. Putting in a bit every month helps spread the impact of the fluctutations in share prices.
The problem with gambling with just a few shares is that commissions/spreads will take a big chunk of your profit - if you are looking to gamble, there are spread betting shops online which will allow you to gamble on all sorts of stock-market related things.