hi Just a week ago I buy a domain for the website. This website has a great list for many keywords. Just one year ago the owner (my friend) decided to 301 to another domain. Now he'll go to sell me this domain and I'm curious what is the best solutions to recover Google position? Did i need to start doing SEO from the beginning?
Yes, You need to start with the beginning. You have done SEO before then you need to re-check the task and optimize your website accordingly.
If redirected one year ago then .... you told already to google that you are using another site so no need to start SEO from first stage. Just continue with your regular link building and other promotional work.
If all the pages are redirected to the domain you have purchased, you don't need to do more work on SEO.