Live Streaming solution.

Hi, Obviously there is a lot of tech guys here, and since I know nothing about "live streaming technologie" I was wondering if you could help me to understand something.

I would like to create a based community website which propose "live streaming classes". The teacher would be able to choose between asking a fee for people who want to enter the classe, leave it free, and, why not, just ask for donation.

The think is, I cant conceptualize in my head, how the streaming part work. Should I consider live streaming services supplier ? or should I host it on my own ?

Is someone enough kind could help me to understand this please ?