Were can teens that are homeless get an apartment or house.

A teen has to be 18 and have money in order to sign a contract/lease/mortgage.

My boyfriend is 19

If he doesn't have money (i.e. a job), then he is unlikely to find a landlord to rent to him. There are usually homeless shelters where he can start with to find rooms to rent.

Why is he homeless?

No one is going to "give" you a place to live, there will be shelters but there are few family shelters so most likely he will go to a mens shelter and you a women's shelter.

There are a few ( often with long waiting lists) though religious groups that offer housing ( more like dorms) where families can live, but they will require strict rules of conduct, and they will normally require work details that they send out, while trying to find you work.