Hi guys!
I've been here for 4 months now and am starting to learn a thing or two.
You can rent apartments very inexpensively if you are staying in the one place for six months. At the moment a tourist will pay $25 upwards / night for a room in Havana.
I do however know quite a few students (foreigners as well) here who are renting either rooms or full apartments for a range of prices varying from $200-$500/month. You don't have to be a student and can probably get cheaper even as a foreigner.
Another solution is couch surfing, which, depending on what style of living you like, can be fine and is unbelievably cheap. (I have a Cuban friend that lets out his Sofa for next to nothing)
Hope this helps!
Jade