The internet has swept all of that away. Now you can buy and sell stocks and shares online quickly, easily and cheaply from between £7 and £12 per trade, without ever speaking to a stockbroker.
Anybody with access to a computer and a bit of spare cash in the bank can do it.
You can make good money from investing in stocks and shares, but you can lose good money as well.
Yet it isn't a complete gamble, and if you're careful, you can shift the odds nicely in your favour.
Here's how to get started.
What exactly are shares?
A stock is a share in the ownership of a company. Once you buy a company's stock, you become one of its shareholders, which means you own a share of its assets and are entitled to vote at its annual meeting.
Importantly, it also entitles you to a share of the profits. This is typically paid in the form of dividends, which are payments made to shareholders, typically every quarter or twice a year.
And if the share price rises, so does the value of your stocks.
Why do companies issue shares?
As companies grow, they often need to raise money to fund the next stage of their expansion. One way is to borrow it from the bank. Another way is to issue shares in the business.
Where are they traded?
Shares are traded on scores of indices around the world, such as the FTSE 100, which tracks the 100 largest companies in the UK, or the S&P500, which follows the fortunes of the top 500 US companies.
You can also invest in smaller UK companies on indices such as the FTSE 250, or the alternative investment market (AIM).
How do you buy and sell shares?
Most ordinary investors now trade shares using an online stockbroker. Once you set up an account, you can buy or sell a stock in seconds (although you should spend a lot longer than that doing your research).
Online stockbrokers also offer services such as company research and investment guides, and as well as let you to set up a dummy account to get the hang of investing before committing any real money.
When comparing sites, check the fees carefully. Some sites offer a flat fee of around £10 per trade. Others give you the option of paying, say, 1% of any trade, which would be attractive to those investing under £1,000, but costly for everyone else.
You can invest using your annual £15,240 ISA allowance, and take your income and growth free of tax.
What are the rewards?
Many beginners start off hoping to make fast money from some hot stock market tip. Calm down. It won't happen. If you do strike it lucky once, chances are you won't do it again.
If you flitter from stock to stock, quickly buying and selling in the hope of banking a quick profit, you will rack up a load of dealing charges, which could wipe out any profit you make.
To make money from stocks and shares, you have to be patient. You should invest over a minimum five-year term, preferably much longer, to allow you to overcome any short-term volatility.
Investment legend Warren Buffett famously said that his favourite holding period is forever. You probably haven't got that much time on your hands, but the longer you give it, the better.
Many novice investors underestimate the importance of dividends. Over the longer term, these can account for roughly 40% of the money you make from investing in the stock market, provided you re-invest them back into the stock, to benefit from compound growth.
What are the risks?
The obvious risk is that you buy a company and its share price crashes, or worse, it goes out of business.
Or there could be a stock market crash, and all the shares you hold fall at the same time. In the autumn of 2008, for example, the FTSE 100 almost halved in value in a matter of weeks.
If that happens, you won't get any compensation. You have to take it on the chin.
There are things you can do to minimise these risks, but you can't obliterate them altogether.
Don't put all your eggs in one basket. Instead you need to build a portfolio of different stocks, to minimise the damage if one fails.
You should also invest across different sectors. Don't start by buying three banking stocks, say, Barclays, HSBC Holdings and Lloyds Banking Group, as all your money will be exposed to the fortunes of a single sector.
You might want to balance that by investing in FTSE 100-listed oil majors such as BP and Royal Dutch Shell, pharmaceutical companies such as GlaxoSmithKlein and AstraZeneca, mining giants such as BHP Billiton and Rio Tinto, supermarkets Sainsbury's and Tesco, or utilities such as Centrica and National Grid.
Think twice before diving into, say, some small technology start-up you've read about. This is a high-risk activity, and you're far more likely to lose your money than invest in the next Amazon or Google.
Is it worth it?
Investing in stocks and shares is riskier than leaving your money in the bank, but the potential rewards are far greater. UK equities have a 99% chance of outperforming cash over an 18-year period, according to research from Barclays.
Over the short term, anything can happen. So start cautiously, until you get the hang of it.
Dismiss any notion that shares will help you get rich quick. The reverse is true: they're a great way to get rich slowly.