You can buy shares through your bank, or through online companys, take a look at the link.
http://www.moneysavingexpert.com/savings/cheap -online-sharedealing
One of the thimgs I woul say to you is, only buy shares with what you can afford to lose, you can make or lose a lot of money trading in shares, I have done it for a few years now, but never be over greedy, if the ahres rise a fair bit and you are happy to take the profit, then sell them don't wait for the price to keep rising, "always leave a bite of the cherry for somebody else"
You should buy shares with a view of medium to long term investment, if you buy in a big company don't worry if the shares drop in value, they will recover so don't panic, some companys give freebies if you are a shareholder, or maybe discounts.
http://www.investorschronicle.co.uk/ResearchTo ols/default/article/20050915/c5ddf468-e91a-11d b-9f1b-00144f2af8e8/Shareholder-perks.jsp
also look athe yield the companys are giving, a company that does give good dividends is Lloyds TSB, just be very careful, good luck and take care.