Start from learning REST API testing. REST is just an architectural paradigm, however most often it is implemented over HTTP protocol. So if you mean such the REST API then I would recommend to learn:
- Some programming language basics
- Learn how to interact with remote services using HTTP(s) protocols in that chosen programming language
- Select some service to practice on (if your current job does not let you use one, you can just find a lot of examples in the Internet)
- Apply common principles of test design to design the tests that you would run if you would execute manual testing for the service
- Code those tests (api tests are the tests which can be converted from the manual to automated state in the most effective way since API is somewhat originally intended to be used from the code)
These are the steps for mastering REST API automation testing skills.
Testing micro services depends on how they are implemented. It might be enough to master REST API testing to be able to smoothly move to micro services conception. However sometimes one would need to learn CI processes in general and some concrete frameworks like Docker.