If you have not worked out with weights before, I suggest starting out with a full-body routine two to three times a week, one exercise per body part, two for lower body. Start with the largest muscles (lower body) ending with the smallest (arms). Start with 12-15 reps per body part (choose a weight that makes the last two reps tough but doable).
A sample routine with ideas for exercises:
Legs (squats and leg press or squats and lunges)
Back (seated row with cables, 1-arm row with dumbbells, or lat pull-down)
Chest ( flat or incline bench press with dumbbells or barbell)
Shoulders (I recommend freeweights for these, as machines force your body into a preset pattern, and the shoulder can be particularly sensitive to this: dumbell over head presses or a combo move of front and side raises)
Triceps: (seated overhead presses or tricep pressdown using the lat pulldown bar)
Biceps (bicep curls with bar or dumbbells)
Abs (you can incorporate sets of various curls between other exercises or at the end of your workout)
The first day, do 1 set of each exercise to get your body used to it. Then go to two sets, then three when you feel ready. By then, you'll be ready for a split routine.
The simplest split is lower body/upper body. Do about 4 exercises for the lower body and 2 per body part for upper body. You can add leg extentions and curls for the lower body. Work lower body 2 x/week (maybe Monday and Thursday) and upper body two times a week (maybe Tuesday and Friday).
If you are not very experienced with weight training (I can't tell from your post if you are an Intermediate weight trainer, or just an intermediate exerciser, or if you have much weight training experience, so forgive me if I'm giving you info on what you already know), you can follow a routine from a book, like books by Rachel McLish or Cory Everson or Gladys Portuguese or even Joyce Vedral (whose own form is abysmal, but who writes good books about routines).
It's a good idea to get a book that shows good form. Not all of them do. I recommend books by Douglas Brooks. He is a stickler not just for effective exercise (one of his books is called "Effective Strength Training"), but for safe execution of moves.
Another book that gives you a better understanding of weight training is Karen Andes' "A Woman's Book of Strength" You may also be able to find other books that show different exercises in the library. Men's Health has some good books with a variety of exercises. "Designing resistance Programs" by Fleck and Kraemer is a good reference if you really want to get into routine planning in depth.
You could also do a "Cathe-type" workout at the gym. Just take a list of what exercises she does in a workout like MIS or PS (the DVD chapter listing can help with this) and transfer it to the gym.
