well, it's a very large "orgnaization" to sum up in a post, but essentially you can enroll in either tricare standard or tricare prime.
if you enroll in tricare prime, you receive treatment at military facilities, from military doctors, have very, very little say in who and where, but there is absolutely no cost to you.
tricare standard is more like your typical hmo. you choose your provider from a list of participating doctors and there are associated copays.
i'm enrolled in tricare prime, and what i've learned (with several medical issues myself) is that you have to have a very proactive approach; do your own research as much as possible, and go into your provider informed, with questions, and ready to take a stance on issues, if necessary. if you know your stuff, they're likely to do what you want.
each military treatment facility is different, each tricare prime clinic is different, and of course, each doctor is different. i had a primary care physician in va beach that i would've rather died before i went and saw; however, my primary care physician here in whidbey is better than any civilian doctor i would've chosen myself, and i will be very, very sorry when i have to move away from him.
a couple of general things to keep in mind are the "standard" exams you get free every year; eye exam, dental exam and cleaning, and woman's exam, all of which you can self-refer to (meaning you can choose any participating doctor to perform these exams, whether you're enrolled in tricare standard or prime). a lot of spouses aren't aware of these benefits.
as far as prescriptions, again i'm speaking as someone on tricare prime, they come at no cost to you, so long as the military pharmacy carries it. if the military pharmacy doesn't carry it, you pay $3 for a generic brand or $9 for a name brand at an outside pharmacy.
tricare is a huge "monster" with so much to know. before i enrolled, i went to a tricare service facility and had a caseworker explain the ins and outs to me as best she could. it was very, very helpful for me. even if you're not around a navy base, they have the tricare service centers at all military bases (i went to an army one), so i recommend your wife, and you, if you can/desire, go in and talk to someone in the service center.
good luck