Keyword Research

[MilesWeb]

How can I research Keywords and analyze competitors' for free

Hey Andrew. 
Here's my suggestion. 
 
First of all, it's important to know that free will comes with certain limitations. Even though freeways will provide you with some valuable insight, you will need paid ways to get deep analysis. 
 
Here are some ways to research keywords and analyze competitors' keyword usage as well. 
The first and most preferred tool is Google Keyword Planner, which provides search volume estimates, competition levels (low, medium, and high), and related keyword suggestions. Another popular tool is 
Ubersuggest, too, offers limited searches per day but provides search volume, competition level, and related keyword suggestions.
 
For competitor analysis, try the SEOquake Chrome Extension, which provides basic SEO metrics directly on SERPs and also highlights your competitors' estimated traffic and organic keywords.
 
As your need for deep analysis increases, it is advisable to go with paid tools. Paid tools will improve your search results, and you can do better keyword research and competitor analysis. Till then, these free tools can suffice for basic needs.