The easiest form of investment to get started with are investment funds (aka mutual funds in the US). They are a form of collective investment (i.e. you invest along with other people in a basket of goods, rather than a single share). The advantage of this is lower cost (buying and selling shares has a cost, with a fund there are economies of scale so it's usually cheaper to invest via a fund than directly in a similar basket of shares), and generally lower risk (if a company that the fund invested in goes bust, you usually lose less money than if you invest in the company directly, because the fund invests in many different companies whereas you'd usually invest in a smaller number of stocks).

ETFs (Exchange Traded Funds) and Investment Trusts are similar to investment funds in that they are also collectives, relatively low cost. The current fashion in investing is to buy 'passive', 'tracker' or 'index' funds (or ETFs), which all follow an index such as the FTSE or S&P. These tend to be lower cost than 'actively managed' funds (where the fund manager tries to beat the index). Vanguard is a popular 'passive' fund manager.

Other types of investments include property (you generally need quite a lot of capital), and more risky types of investment such as forex trading, spread betting, etc. Even experienced investors tend to consider these risky.

Investments have done reasonably well over the past year in some areas (some UK income funds are up 8% in the past 12 months), not so well in others (a FTSE All Share tracker is only up 0.6% over the year). Investing is not risk-free, and generally speaking there is no guarantee to make a profit. You could also consider saving in cash, but with interest rates as they are now, you'd probably be worse off in real terms by the end of the year than you were at the beginning (because interest rates are generally lower than inflation)

Some investment brokers in the UK include: rplan (disclosure: I work for rplan), Hargreaves Lansdown (the largest), Fidelity, Nutmeg (another startup).

As others have mentioned, it's definitely worth doing a bit of research to find out more about how things work. If you don't mind the shameless plug, we have a 'guide to investing' available on our site which we think is quite a good overview of what's available (it's fairly UK-specific though): https://www.rplan.co.uk/investment-guide (note: registration required, let me know if you'd rather not register and I can send you a copy).