I use
Iweb which is part of Halifax. £10 flat fee with no minimum no of trades. You can also shelter shares in a self select ISA, althought there is a small admin charge.
Personally, I get tips from the Telegraph money website or the BBC pages and the
breakout charts someone linked to a while back.
Investors chronicle would be a good investment if you are serious.
The markets are a bit volatile atm, but there are some good bargains out there if you look.
Are you after a long term investment (blue chips) or day trading (more risky, but potentially better returns). As Paul says decide how much you can afford to lose and then anything you gain is a bonus. Also remember to take your gains on a regular basis (which I don't)! A 50% gain is only on paper until you actually realise the profit - as has been seen over the last couple of weeks.
HTH.