Get on something is usually used with a noun, like "get on the horse". To "get on" with someone means that you get along with them. To "get into" usually means to physically get into something, "She got into the car","she got into the course" Hope that helps.

Get into can also mean to gain interest in something, like get into reading or get into drawing. Get into would sound weird to say like get into a person but you can be into a person meaning you are interested in them. "Are you into him?" Meaning are you interested in him would make sense or "I think she's into you". Have you heard of the movie called "He's just not that into you". And to get on with someone sounds like something they say in the UK but in the US we do not say get on with someone we say say get along with someone. Get on to me means literally physically on something, like getting on the bus etc.

Ashley mentioned "to be into someone" which is perhaps the variation your teacher meant (you are lesbian if you are into girls). * he is into guys; he is not into girls (so he's gay) * the child is into trains (likes trains) Another variation I want to mention is "to get it on with [someone]", which is a sexual thing and not the most polite way to say it (I get mostly rap song results on Google). See #3 here: http://idioms.thefreedictionary.com/get+it+on * he asked her if she wanted to get it on (wanted to engage in behaviour not appropriate to describe here) And "get on" or "get into" like that are used for humans entering something. Here "get on" is mostly for vehicles, and "get into" can be used for other things like buildings as well. "get into" sounds a bit more forceful to me. * get on the bus * get into the bus / get into the house