The best way the learn ASL is to register to take ASL classes together in-person (not online, or from a book... which really doesn't work).
Depending on where you live (size of city etc) ASL classes may be held at a Deaf Centre, School for the Deaf, school, community centre etc.
You'll want to find a class that is taught by a native ASLer who is either Deaf themself (preferably) or is a CODA/SODA (child/sibling of Deaf Adult)- meaning some one who has been signing for many many years, often their entire lives, uses ASL as their primary means of communication, has taken instruction/classes teaching them how to teach the curriculum provided (this is often done "in-house" bases on specific standards set out by the province/state/city etc). Also it's important that whoever is teaching the classes is an active member of the local Deaf/(Hoh) Community in your area and is willing to help you immerse yourself in the community as much as you wish/are able.
Don't "worry" about how you'll communicate initially if you're teacher is Deaf ... the teachers will have hand outs, write words on a white/chalk board, and often will have an ASL/English interpreter come in for the first part of the first class to interpret for them the initial "rules", questions about how to contact the office if you'll miss a class due to illness etc, how the course will be marked etc.
For prospective students who are Hoh or Deaf themselves, finding a class taught by a Hoh or Deaf teacher also helps ensure that it will be a "voice off" class ... meaning ONLY ASL will be used in class (and writing on a board) - however no instruction will be giving orally, meaning that your hearing won't negatively impact you're ability to participate in class ... actaully many of the skills you've picked up regarding "filling in the blanks" when you miss something spoken etc, will now be an advantage in learning ASL!
Do beware of some "ASL Classes" that might be offered at community centres etc by hearing people who've been through all the levels of ASL 101-302/3 and now think they can "teach" ... these people so NOT have the fluency required to teach (but somehow, these "classes" appear occasionally ... usually until the Deaf/Hoh community finds out and talks with the "teacher", explaining that what they are trying to do is both wrong and disrespectful
There are some good books & DVD series out there ... the BEST of which is called "Signing Naturally" - in fact it's often the basis from which many ASL courses are taught. That being said, I can't stress enough how very very important learning from someone who's primary language is ASL will be. Learning ASL from a book, is a lot like trying to learn English from a dictionary - while you can learn some words/signs from a book which might allow you to identify objects (apple, mum, dad, bus, car etc) , you can't learn ASL the language (verb tense, spacial grammar, the way to connect ideas together etc) from a book.
I think it's FANTASTIC that you are in a position that your fiancé is interested in you both learning ASL
Incidentally - there are many more classes that someone must take after finishing the "standard" ASL classes (101-302/3) to learn how to interpret English to ASL and vise versa (it's a fun, but challenging job). Many larger colleges/universities now offer ASL/English interpreting diploma or degree programs which might be of interest to your fiancé - they may even wish to consider being an interpreter as a career (interpreting takes place in a variety of settings including educational (kindergarten -> university) Medical (doctor's office,hospital, mental health, etc), industry, retail, communications, government, legal, .... basically anything you can think of - it's likely an interpreter will be needed in that position making it a VERY reliable job, even in a tough market!
let us know how things go !
Once you starting learning, many of us have webcams etc in order to communicate with each other in ASL - great for beginners looking for some practice and help outside of their ASL classes