It's reckoned that over 10m people own shares in the UK thanks to big privatisation issues like British Telecom and British Gas in the 1980s and the building society demutualisations of the 1990s. However, only a small minority of people, less than 1m perhaps, actively buy and sell shares on the stock market on any sort of regular basis.

At the Motley Fool we think that's a great shame. Getting involved in the stock market is a great way to build wealth, and it can be fun and educational too (yes, really!).

There are plenty of reasons why people don't invest in shares. But many people are afraid of the stock market because they think it's too complicated. The good news is that over the last several years it's become much simpler, and a lot cheaper, for private investors to buy and sell shares.

To understand what has changed, a brief explanation of the three main types of stockbroker can help put things in perspective:

1. Full-Service Broker

Here you hand over your money to a broker and he decides which shares to buy and sell. You pay handsomely for this privilege and you usually need a hefty amount of money to even get in their front door. These brokers are often accused of 'churning', meaning they frequently buy and sell the shares within their clients' portfolios. For the most part, these portfolios won’t do any better as a result of this frenetic activity. However, the broker will earn a lot of commission!

2. Advisory Brokers

This type of broker will let you buy and sell whichever shares you want, but they will also give you lots of suggestions about what trades you should make. They might recommend switching from Amalgamated plc into Agglomerated plc, as they've just been rated "accumulate carefully" by Trade, Grabbitt and Run. As with full-service brokers, it is in their interest to persuade you to trade more often, as they get more commission that way.

3. Execution-Only Brokers

As the name implies, these brokers will simply execute the trades you ask them to. So it's entirely up to you to decide what to buy and sell. Naturally, as you're not paying for any advice, this type of service is the cheapest of the three and ideally suited for the Internet.

Up until the mid to late 1990s execution-only brokers only offered services by phone or via a bank branch. Typically, you were charged around 1.5% of the value of each trade as commission so, for example, a £5,000 trade would cost you £75. Online brokers completely revolutionised this process by charging a flat fee per trade. These days you can trade shares worth tens of thousands of pounds for around £10!

But enough of the preliminaries, let's get down to business. We're going to tell you what to look for when you're picking a broker. And when we've told you that, we'll tell you about one online broker which we believe ticks all the important boxes.

Next article: Choosing A Stockbroker