Ever dreamed of being a millionaire? Lots of people would like to aim for a million – but putting that dream into practice is not necessarily an easy thing to do.

Even from a standing start, I think someone could try to aim for a million by drip feeding money into carefully chosen blue-chip shares on a regular basis.

Here’s how.

Being the tortoise not the hare

Some people have a fantasy about putting a little money into the stock market, finding a brilliant small company set to explode, then watching their investment soar in value.

That can happen – and occasionally it does. But a lot of small companies, even seemingly promising ones, end up going nowhere.

Rather than focusing on speed, I think an investor can focus on taking a realistic approach to investing by using a long-term approach based on finding brilliant businesses that have attractive share prices.

That way it may take many years to aim for a million – but hopefully it can be a realistic goal to aim for.

Building wealth over time

To put that into perspective, let me use a practical example.

Say someone invests £500 per month and compounds it at 10% per year.

How long would it take them to aim for a million?

After 30 years, that approach ought to have increased their portfolio to over £1m.

Choosing shares to buy

So yes, this is a long-term approach to investing.

But I see it as a practical one.

Still, is a 10% compound annual growth rate over the long term realistic? After all, dividends are never guaranteed and share prices can go down as well as up.

I do think a 10% compound annual growth rate is realistic, but it helps to focus on high-quality companies selling at the right share price.

For example, one share I think investors should consider is Ashtead Group (LSE: AHT).

At first glance, this might not seem too exciting: the company operates in the unglamorous world of plant hire and its share price has grown just 5% over the past year.

That pales compared to the 21% growth during that period of the FTSE 100 index, of which the company is a member.

But I think Ashtead has quite a few things going for it.

Demand for plant hire is high, due to large infrastructure projects and housebuilding. There are only a few sizeable groups in Ashtead’s key US market – and it is one of them.

The company has a proven business model, a clear strategy, and a sizeable client base.

Building can be a cyclical market. So any downturn in US construction could be a threat to revenues and profits for the company. But over the long term, I expect the business to perform well.

Getting started, today

If someone aims for a million, of course, they need a practical way to do so.

A useful first step can be selecting a suitable share-dealing account, Stocks and Shares ISA, or trading app for their needs.

After that, they can start to identify the sort of high-quality shares at attractive prices I mentioned above, as they aim for a million.