Hi there!!
I lived here for 18 months before and during the first part of the revolution, and have just moved back to help rebuild the country through teaching. Libya is an amazing place with amazing people, and very friendly towards foreigners - as long as you come with the right attitude - which is to learn from Libyan people! :-) My best suggestion to you, apart from attending a Libyan arabic course, is to make friends with Libyans wherever you can - in your workplace, in the street in shops, etc. The best way to learn the language is to practise speaking it in the street as soon as possible. The classroom can only help you so far - the rest is up to you. :-) Having learnt a number of languages apart from Libyan, and lived in a few places before coming here, my experience has taught me that this is the best way: "divorce" yourself from your own culture as much as possible, and soak yourself in the language and culture of the local people. That is the quickest way, not only to learn the language, but also to learn more about the culture and the people - and even how to not only survive here, but also to THRIVE!! :-) Every blessing to you both, as you integrate into libyan society... :-)