Backlinks (i.e. external hyperlinks pointing at your website) are important.
Go for quality in-bound links from high authority websites.
Here is a checklist of ways to get more backlinks:
Offer to write a guest blog and include one or two anchor text links within your blog.
In Google, search for: your keyword + inurl:write-for-us
[If you try doing this search, the results can be quite surprising].
Tell a website owner about a broken link and suggest your website as a replacement.
To find relevant websites with links, search in Google for:
your keyword phrase + inurl:links
Write detailed, long form content on a specific topic that you want to be found for. Ensure that you optimise the page, using the techniques that you will find within my SEO Guide.
Promote this content as widely as possible, i.e. via social media and your newsletter. In addition, link to this content from popular pages in your own website.
Use a list approach. Interesting, helpful, up-to-date lists get more backlinks (hint, hint).
Another approach is to write guides. The more in-depth, the better. A useful guide is likely to get backlinks.
Create infographics which link back to your website. Visme is a creative way of doing this.
Include interesting / relevant websites within your pages and posts; email the webmaster / blogger and tell them that you have done this. There is no need to sell them on backlinks. They are quite likely to mention you via social media and some of them will link to you.
Send out press releases and include a link to your website.
Think about the trade / professional associations that you belong to. They probably allow backlinks.
Ask your suppliers if they will kindly link to you.
Internal links within your website
Don’t forget to include plenty of internal links within your own website. The search engines will be grateful.
Finally, do not buy backlinks.