First of all you want to own the domain. Buying the domain will show search engines that you are doing it for something other than fun, and that you are trustworthy. Search engines only promote sites that they believe are trustworthy sources of information. When you do not own your domain you could just be anyone, search engines don’t know if you are worth promoting. So if you want to rank well, do yourself a favor and purchase a domain.
Second, post original content. Don’t copy content off of other blogs or sites. Posting original content allows your blog to be seen as trustworthy. If you post original trustworthy content that solves problems that people are searching for, you are more likely to rank well. Also adding original media such as videos, podcasts, images, etc. will also make your blog more prone to higher rankings on search engines.
The last tip I will mention is back-links to your blog. Having links from other websites related on the topic back to you are very beneficial for high rankings. Going back to being trustworthy, if other sites trust you that shows search engines that you are in fact trustworthy. Also, never buy back links. The source makes a big difference. One back link from a high ranking site is more valuable than one hundred back links from insignificant blog. Don’t forget to back link to your own blog. Keep the readers on the blog as long as you can.
I hope this helps with any basic questions you have about ranking well in search.