no gym & small apartment weight lifting?

Maybe TRX , a few kettlebells and a sandbag

A set of adjustable dumbbells? A Swiss ball? You can use the latter for many things, including as an unstable bench for your chest presses.

I agree. You can get a great start with these two items.

I have this book called, "You are your own gym" by Mark Lauren. It is a good book. He has tons of pictures of dif. workouts to do with just your body weight or things around the house. It is a good book.

I was just gonna say the body weight exercises thing

resistance bands

and/or

strength training dvd, e.g., 30 day shred

A set of adjustable dumbbells? A Swiss ball? You can use the latter for many things, including as an unstable bench for your chest presses.

I agree. You can get a great start with these two items.

The Swiss ball can be used for pushups, squats, lower back exercises, etc. I once had an electronic jump rope, which would be good for a small apartment.

try this website: http://www.youtube.com/user/insanehomefatloss?v=h30dWmbvsfk, it looks great

Using your body weight as resistance is fine until you can do 9-11 reps etc. for each exercise but at that point you need to increase the amount of resistance and the only way your going to do that is by adding weight. If your not doing weighted exercise your pretty much wasting your time.
Here is a post I made to another member that asked a similar question. You can get a 40lb set of Cap adustable dumbbells for $30.00 (and add additional plates as needed for $2-4 dollars each. a pullup bar for $18.00 and an exercise ball for $10.00 at walmart. You can get just as good of a workout at home using these inexpensive things that don't take up any space as you can at a gym.

Ok here is the program/split. To keep it simple try to do 8 reps for every set. If you can do 10 reps, raise the weight for the next set, if you can only do 7 reps or less ,lower the weight for your next set. Also try to limit your rest periods between sets to between 1 minute and 1 minute and 30 seconds. I choose to do my cardio and abs on my off days but you can mix them in to fit your schedule/ needs etc. Also please dont be intimidated by lifting!! (we all were when we started but quickly realized that there wasnt anything to be scared of)

Monday: Legs-
Squats x 3 sets. http://www.exrx.net/WeightExercises/Quadriceps/DBSquat.html
Lunges x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/dumbbell-lunges
Step ups x 3 sets. http://www.muscleandstrength.com/exercises/dumbbell-step-up.html

Calves-
Seated Calf Raises x 3 sets. http://www.muscleandstrength.com/exercises/seated-dumbbell-calf-raise.html
Front Raises x 3 sets. http://weighttraining.about.com/od/exercisegallery/tp/frontdumbbell.htm

Tuesday: Back-
Pull Ups x 3 sets ( use a chair and push off it with one foot to assist you as much as needed to complete each rep.)
Dumbbell Rows x3 sets. http://www.bodybuilding.com/exercises/detail/view/name/one-arm-dumbbell-row
Bent Over Rows x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/bent-over-two-dumbbell-row

Biceps-
Curls x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/dumbbell-bicep-curl
Concentration Curls x 3 sets. http://www.muscleandstrength.com/exercises/concentration-cur.html

Thursday: Chest-
Bench press x 3 sets. (use your bar)
Incline pushups x 3 sets ( use the bottom step of any set of stairs and do as many as possible for each set)
Dumbbell Flys x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/dumbbell-flyes

Triceps-
Extensions x 3 sets. http://www.muscleandstrength.com/exercises/one-arm-seated-dumbbell-extension.html
Kickbacks x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/tricep-dumbbell-kickback

Saturday: Shoulders-
Shoulder Presses x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/dumbbell-shoulder-press
Front Raises x 3 sets. http://weighttraining.about.com/od/exercisegallery/tp/frontdumbbell.htm
Lateral Raises x 3 sets http://weighttraining.about.com/od/exercisegallery/tp/frontdumbbell.htm

Traps-
Shrugs or Seated Shrugs x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/dumbbell-shrug

Lower Back / Glutes- ( Yes its leg exercise but you dont want to do deadlifts and squats on the same day)
Dead Lifts x 3 sets. http://www.bodybuilding.com/exercises/detail/view/name/stiff-legged-dumbbell-deadlift

I have a very small 1 bed flat/apartment. I have a pair of dumbbells and resistance bands. I do my exercises in my lounge 3 - 4 times a week.

I didn't see any suggestions for a pull up bar.

Maybe that's because unassisted pull ups are hard for most women. The OP sounds like a newbie.