Working more hours each week is one way to try and eke out a second income.

But an approach I prefer is simply to invest in shares that one hopes will pay out dividends to shareholders in future.

If I had under £10,000 in savings, I may well still have enough to get going on that approach. Here is an example based on investing £9,000.

Using cash to generate dividends

First let me explain in more detail how this approach might help me build a second income.

When companies generate surplus cash they have a number of choices as to what to do with it. They might build new factories, for example, or fund the takeover of a rival.

One use is paying dividends to shareholders. Companies listed on the London stock market spent well over £1bn per week on average last year paying such dividends.

Simply through buying a share in a company that pays dividends, I am entitled to any ordinary dividends it declares while I hold them. Still, dividends are never guaranteed no matter what has happened in the past, so I would diversify my shareholdings across a number of companies. My £9,000 would be ample to do that.

Building bigger passive income streams

Already I like this plan. If I could achieve a 7% average annual dividend yield, for example, I would hopefully earn 7% of my £9,000 each year: £630.

But I could try and earn even more, while buying the same shares and still using my original £9,000 investment. To do that, I would reinvest the dividends – a straightforward but potentially lucrative investing move known as compounding.

If I compounded £9,000 at 7% annually, for example, after 20 years I ought to have a share portfolio worth almost £35,000. At a 7% yield, that size of portfolio would be big enough to earn me around £2,437 as an annual second income.

Starting today

Time can be the friend of the investor, so I would start investing sooner rather than later as long as I could find quality income shares to buy at the right price.

One share I own that I think fits that mould from my perspective is Legal & General (LSE: LGEN).

The financial services market is large and I expect it to remain that way. Thanks to a focus on the retirement end of the market, Legal & General benefits from long-term growth prospects, substantial cash flows and demand that I expect to be resilient.

It can use its strong brand and large customer base to try and make the most of its position. So far that has worked well – not only is the firm consistently profitable, it also offers a dividend yield of 9.2%.

I do see a risk that turbulence in the financial markets could lead some clients to end their policies, hurting profits.

But I plan to hold my Legal & General shares in my Stocks and Shares ISA for the foreseeable future – and hopefully build my second income.