The truth is there really is no definitive answer to this question. Individual ways of improving a websites search engine performance can vary drastically dependant on many factors. Making sure the websites architecture is thoroughly and rigorously checked and audited is your first step when coming up with a strategy. The more thorough and in depth your audit, the better your chance of rectifying all of your sites issues in one fell swoop. Proper auditing can save you having to keep coming back to the same areas of your site to fix small issues that could have been identified and rectified earlier.
The next step is to properly envision and quantify what your website's goals will be and what kind of visitors you want to attract to your site. Essentially this step is all about understanding your sites visitors and their journey. Doing things like proper keyword research to find the most relevant search terms, making your site mobile friendly in order to improve your visitors “user experience” (or UX) better and making sure that the content on your website is clear, easy to read and relevant to exactly what it is you do and what you offer.
The next step is to make sure that, in the eyes of Google, your website is a trusted and highly referenced authority on whatever keywords or topics your website is attempting to target. One way this can be achieved is by undertaking outreach with third-party sites and generating an online buzz to get not only traffic, but also links from external sites referring back to you as an authority that their visitors can trust.