Paper trade with City Index or Capital Spreads for a while. You can open a "dummy" account with these guys and they'll give you 10k of monopoly money to play with. See how you do for a few months. You can afford to frighten yourself this way (like using a flight simulator instead of trying it in a real airplane).
If you want to jump straight in, Finspreads will let you open an account and trade at 1p/point for the first 8 weeks (but you can't place stops on less than 50p/point, as I remember). This way you risk real money -- and that will affect your psychology -- but without risking much.
For spreadbetting, all these firms are OK.
Good luck -- and another thing -- only do it if you enjoy it.