This is a graph of the search performance of pocketoperations.com in its first two weeks after launching.
This graph has really surprised me. Everybody says you should expect a long lag time doing SEO. Also surprising is the site is brand new and everybody says it takes a long time to establish search authority. It's early days but it seems to be seeing steady search growth from the outset.
How can you replicate this? I don't know for sure. I can only tell you the factors that led to this. The tl;dr is: find an uncrowded niche, do research in communities, follow best practices.
Let's break it down.
I didn't set out to find a niche with low-competition. I was already working on pocket operator apps and it was only when I started using ahref's free keyword generator that I realized the space was relatively unoccupied. It would probably be better to use a keyword volume tool from the beginning to find something you have a chance at as part of your initial validation of a business idea.
I spent a lot of time in /r/pocketoperators learning about what people there care about. This was easy because I'm genuinely interested. My research was fairly systematic (taking notes). I did the 30 to 40 hours of note taking research recommended by Amy Hoy, over a period of several weeks. This gave me a very clear idea of the most important topics people are interested in around pocket operators. So that's what I wrote about on the site. Every page represents one of the main topics people discuss.
The article by @jdnoc is the most concise article on SEO I've seen. It isn't filled with marketing blarg and up-selling. It gives you the most important and simple tips first, like getting tags right. It goes into just enough detail without being confusing or complicated. I closely followed Jordan's method.
So that's a summary of what I did to get this small win in search. I am trying to replicate it now with a different site, and of course I'll keep working on pocketoperations.com in the mean time.