This is the most important search engine optimisation strategy you can spend your time on. When another website links back to yours, Google sees this as a positive vote for your website, and will take this into account when determining which websites should be at the top of the page.
The more websites you have that link back to you, the higher your website will appear in the search results. But there is one main factor to consider with this strategy, and that's the credibility of the websites linking back to yours.
The quickest and cheapest way to get websites linking back to your website is to send them an email and just ask for it, but what type of websites should you request links from? In general they should be similar in topic to your website, so as a web designer you might request links back from websites that talk about web design, marketing, attracting new leads and customers, etc. The best plan is to ensure those websites are ones that you would recommend to your users, that your users would find useful and that add support to your website.
A medium/long term strategy is to publish high quality articles on your website that others will link back to.
So what should you write about and how often should you write? One article a week is a great start. Aim for 500-1,000 words and write about what you know. Topics your potential customers will expect you to know about and after reading your articles they will come to trust you.