What are pre-requisites for working at a Uni?

I have worked in Japan for 3 years. First at an Eikaiwa and now at a well established Kindergarten. In the future I want to possibly work for a University. I was told something like I need published papers, and possibly a Master's degree.

How would I go about publishing a paper, and is it true about the Master's degree?

Thank you!

The requirements differ depending on the university and the position.

How would I go about publishing a paper, and is it true about the Master's degree?

For many universities, the Master degree would be a minimum. Nowadays, things are more competitive than ever, so assume your competition will have Master degrees or PhDs in linguistics or similar.

For the paper? Conduct original research in linguistics or a related subject, then write it up and submit to a peer reviewed journal. The Master degree is almost certainly considerably easier.