I like to start with Google first, because Google looks at more of the words within our blog post and tends to keep content evergreen longer. This method is so simple and I learned it from Lena over at WhatMommyDoes.com. Simply go to Google and start typing in a couple words related to your blog post. It will give you suggestions of what people are searching for – hello, keywords!
Of all the tools listed in this article, Moz Link explorer is an old one & quite popular. If you want to compare backlinks between two or more domains, Open Site Explorer is worth trying. This tool works best when you have a paid account of SEOMOZ though a free version of this tool is good enough to get you started checking the backlinks of your site and the sites of your competitors.