I am fluent in English and Norwegian and I do understand some French. I am also able to read greek letters, but I do not know the language. Will these skills help me in any way?
Hahahahhahahahahahahahahahhahahahahahahahahahhahahahahahahahhahahahahahhahahaha. (I may be a little drunk here but that was good)
This is crude, for sure, but my good friend is Arabic and his older brother used to say, "tee-zee-muftu-ha" to us all the time. I have no idea how to spell it, so that is phonetic. But it means, "your ass is open." It's very innapropriate, but we were 14 year old kids and thought it was pretty funny that we could say this in front of our non-Arabic parents and teachers and get away with it. In algebra class our professor would let us choose the variables used, we always picked "T" and "Z". When the teacher said them, so, you take the sum of "T" and "z" ... We would yell out "MUFTUHA" and we thought we were super funny and clever. Even more aside: we had a priest (I went to catholic school) that called Jesus "The Master." Whenever he referred to him as The Master we would all yell out "Bater!" -pretty sure we are all going to hell. How does this help with your question? It doesn't. But thank you for the trip down memory lane. Good luck learning Arabic!
I've studied Arabic for 5+ years now. Firstly, forget everything you know about any other language because it won't help you. To get started learning the alphabet, here's a good video that shows both how the letters sound and how they fit together and how they look in different positions in words
Grammar is a whole different ball game. The purest form of the language is the Quran and it will have the end voweling for the 3 grammatical cases (nounal, accusative, jussive). Sentence structure is almost always Verb - Subject - Object. To build vocabulary, start with the 3 letter root and apply it to the 10 different verb forms in this chart http://arabic.desert-sky.net/g_vforms.html To build listening, BBC Arabic has news clips with attached vocab.
This is as close to a crash course as I can give you over the internet while I'm at brunch but I hope it helps a bit!
French, if you're really good at it, will help you a lot with Lebanese. If you know Spanish, it will help will Moroccan. I'm not sure what resources are available in Norwegian, but I bet there's not a lot. Some background: I studied Arabic for three years in college, and I've forgotten more than I remember. There is a severe lack of English resources on Arabic, but that's been improving since 2001. GLOSS by the Defense Language Institute has some fantastic idiomatic lessons that I'd recommend: https://gloss.dliflc.edu/ ~ most of them are based on real texts. The best texts and dictionaries available are in French because of historical factors. The first thing that you should know about Arabic is that the 'standard' (fus-ha) is kind of like a lingua-franca between nationalities. Each country and region has its own quirkiness. Here's an example: زوجة - zow-dja : wife Because of the large geographic area that Arabic is spoken in, and the enormous history that surrounds it, the above word could also be said as: جوزة - djow-za : wife It's a lot like "ask" vs. "aks" in English. The problem with consonant-switching (I know there's a linguistic term for it but I don't remember it off the top of my head) is that three three consonant patterns (in general) make up the base-unit for all morphology Let's take the classical example of 'to study' : درس مدرسة : a place for studying (i.e. a school)
درَس : to teach You can see the consistent elements in there, the D-R-S. If you 'double' the R, it becomes more intensified or reversed, from 'to study' to 'to teach'. That is one way of about twelve to extrapolate a verb from its base unit. Maybe you could see why the consonant-switching makes spoken Arabic really difficult for beginners. I'd recommend A New Arabic Grammar by Heywood - my Anglophone college professor would go through it every year as it's an excellent academic overview. http://www.amazon.com/New-Arabic-Grammar-Written-Language/dp/085331585X/ref=sr_1_1?s=books&ie=UTF8&qid=1436059900&sr=1-1&keywords=anewarabic+grammar&pebp=1436059905729&perid=10WJ910B3MX9YC1VK4EM
You could get some short-term, very rapid progress by only learning how to speak it. But very soon, you'll run into a word that you don't know and you'll need to look it up. Or you'll come across a zebra that you need to read. Take the literate approach and learn to read and write it as well, it will help you later on. 
I studied Arabic my freshman year of college. I've forgotten a lot of what I learned, but I've been wanting to revisit the language and continue learning it. If you're interested in studying and learning it together, let me know! The book series we used was very good, so you may want to look into buying the first one or two. Alif Baa concentrates on teaching you the alphabet, and some basic words, and the others (Al-Kitaab Part One/Two) move onto teaching you how to hold conversations and grammar. Something worth considering is that "Arabic" actually refers to multiple dialects, but some of them differ enough from the others that they may as well be considered their own language, much like Spanish and Portuguese. The aforementioned book series concentrates mostly on al-fusha (pronounced like foose-ha), which is the type of Arabic used to write the Quran (see Classical Arabic). In terms of usefulness, this is considered by most a good place to start off, since: - It's the formal language used for things like news, lectures, books, etc. - Most of the Arabic-speaking world knows it (although from what I understand, you might get some odd looks for using it in casual contexts) - It's supposedly a good point for moving on to the other dialects once you know it You may also want to look into getting an Arabic dictionary after you learn the alphabet. The one I used in college was the Hans Wehr Arabic-English dictionary.
I would love to learn it with you! How would this work? Voice chat? It might be hard for me to acquire those books, since I live in Norway and the supply of introductory books of Arabic in English is not that large. Internet resources (youtube videos?) and more standardized books, such as dictionaries, would be easier.
Just realized that I think this never posted! Voice chat and e-mailing in Arabic. Maybe also, after some practice, reading books? I live in California, so the weekends might be the easiest time to talk by video. I'll look around and see if I can find us some online resources for learning. I'm sure that there are some good ones out there.
Well first and for all forget the letter P, it does not exist. Pepsi Cola is Bebsi Cola and Pizza is Bizza. Now to move on, arabic is super hard to learn, trust me i have tried, didn't try to hard but i can read in arabic seeing how i speak Farsi(Persian). But still the grammar and everything is super advanced compared to both Swedish, Farsi and English if you ask me. But if you want to learn it, go for it! Don't let anyone stop you!
I tried teaching myself Arabic a while back. I found the youtube channel Learn Arabic With Maha was very useful. Maha is a Palestinian expat living in Italy who teaches Arabic for a living. She's a lot of fun; even if you can't understand Arabic, her videos are still enjoyable to watch.
I second pimsleur. I've been listening to the audio part while i drive and i've learned the basics of Arabic without taking any time out of the rest of my life. I do spend alot of time driving though.
I personally learned it to a degree via the Michel Thomas audio courses. Unfortunately, I lost most of it, but the courses (iTunes versions cost me ~$170 altogether) get you excellent grammar, but not a lot of vocabulary. I wholly recommend Michel Thomas courses.
I will start by saying I don't know Arabic. I do know 4 and speak 3 different languages. The easiest way to learn a new language is when it has a relation to the language you already know. I don't know if Arabic has a relation to the languages you already know but if you're looking for a place to start I'd go to Duolingo. I've only heard good things about it, but haven't used it myself yet. Other then that I'd say watch movies in Arabic with subtitles in English and later the other way around.