One of the easiest ways to convince people is to simply do it, if you can get away with it.
Once they see how much easier it is to refactor something or to tell where a problem came from, others will ask you and follow your approach.
You probably shouldn't write tests for all existing code at once, but instead you can develop your next feature by writing tests first. Developing TDD-style often takes only minimal more effort and leads to a more robust and thoughtful solution.
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One of the easiest ways to convince people is to simply do it, if you can get away with it.
Once they see how much easier it is to refactor something or to tell where a problem came from, others will ask you and follow your approach.
You probably shouldn't write tests for all existing code at once, but instead you can develop your next feature by writing tests first. Developing TDD-style often takes only minimal more effort and leads to a more robust and thoughtful solution.