[GianFabien]

Once you enroll in a PhD program, you can easily get adjunct lecturing work and TA work. Which sets you on the teaching path. The conferences and seminars you attend and the papers you publish create the network of connections.

Perhaps you are at the early stage of your PhD and haven't yet explored the multitude of opportunities. Talk to your advisor(s) about your long-term plans. I'm sure you'll get useful advice and support.

[taubek]

I was actually to old. I was 30 when I enrolled. And there was some rule to become TA you must be under 30. It was a long time ago.