Search engine algorithms are changing all the time, so this answer can always change, however there are key ways to ensure your site will rank better for your chosen keywords.
Essentially your content needs to be as relevant and useful for the user as possible. Users on search engines are essentially Google’s customers, and your site is Google’s product. Google needs to ensure the product they are offering is of good quality and relevant, otherwise their customer will stop using them.
So then how do you ensure Google knows your product (or site) is what people want to find?
Making sure your site has good, quality and engaging content that is kept up to date is one of the key factors that search engines will look for. Make sure to include your keywords throughout the content in a way that is still relevant. Having dedicated pages on your site for specific keywords or services you want to be found for can also help massively.
This can be any kind of interaction with your online presence – whether through reviews, social media, clicks or time spent on your website. If you have a high bounce rate, where people instantly leave your site after clicking then this can have a negative effect. This is why ensuring your site is engaging and relevant to what someone is looking for is so important.
This is essentially a matter of driving relevant and quality links to your site or specific pages. Usually achieved through posting on article websites, forums or blogs. It also involves internal links throughout your site. So having a blog for instance and writing meaningful posts that link back to your service pages can really help.
Site Performance / Speed
Making sure your site loads at a decent speed will improve user engagement and bounce rate so search engines will always look favourably on this. To improve your sites speed you would need to look at things like: image optimisation, the quality of your web hosting, script loading / optimisation, reducing the number of plug-ins or widgets being used and having a well built site structure with clean coding.
Tags / Correct Code Markup
Ensuring your site is built correctly is paramount to allow your site the best possible chance of being indexed. Any incorrect code or missing tags can have an instant negative impact on your sites ability to be found and they can often be relatively simple, one time fixes to resolve. This can include: meta tags, robots.txt file, a sitemap, schema markup / tags, alt tags and more.