Here I am going to enlist some points to do SEO for your new website.

1. Choose Your Domain Name Carefully.
2. Select a Reputable Web Hosting Provider.
3. Perform Keyword Research.
4. Plan Out Your Site’s Architecture. 
5. Use a Mobile-Friendly Design.
6. Target Primary Keywords for Each Page.
7. Optimize Page URLs.
8. Optimize Title Tags.
9. Optimize Images.
10. Optimize Headings.
11. Optimize Text on the page.
12. Write Unique Meta Description.
13. Link to Other Pages on your Website.
14. Submit Your Sitemap to Google.
15. Create an SEO Plan for the future too for better result.

SEO is a long term, ongoing process. So, for this continuous process you can do the work on your own or you you can hitre a Digital Marketing Agency to avail the services of SEO.