Ladies don't be scared to train your upper body as well as your lower and cardio. Lifting weights to build your back muscles isn't going to turn you into a bulky machine - it doesn't work like that. From an aesthetic point of view it can help you create your proportions to give the illusion of a slimmer waist, as well bring definition to your muscles. From a functional point of view making your lats, rhomboids, lower traps and erector spinae stronger it will improve posture, stabilisation and movement.
My top 5 exercises are:
1/ Chin Ups
Assisted or unassisted these are great. I would advise getting yourself a resistance band to assist you rather than using the machine in the gym as it makes you engage the muscles a lot more and gets your body used to pulling up your body weight. The grip is a narrow one with your palms facing each other. Make sure you keep your shoulders relaxed, engage your lats, retract the shoulder blades as you pull up. Try not to hunch your upper back over. As you lower down don't drop into the shoulders but also keep a slight bend in those arms. Core tight.
2/ Bent Over Row
I prefer Barbell for these but you can use dumbbell. Form is everything here before you even think about lifting heavy. Make sure you keep your chest up, slight bend in the knees, bum pushed back and head in line with the spine. Keep the back flat with the arms straight down in front at about 45 degrees. As you pull the weight back think about driving the elbows back, squeezing the shoulder blades and engaging the rhomboids.
3/ Seated Row
This can be done on a specific machine or using cables but both will do the same thing. You want to drive the elbows back squeezing the shoulder blades. You want to pull the handle towards your tummy keeping your shoulders back - on the return don't let your shoulders drag you with them.
4/ Lat Pull Down
A great one to develop width and as the name suggests working on your lats. Lean slightly back from the pelvis and pull the bar towards your chest. Initiate the movement from the scapula retracting not your biceps. I like to slow down the concentric phase of the movement (lowering of the weight).
5/ Dorsal Raises / Hyperextensions
One for the lower back. Laying on the floor prone position (face down) your hands can be resting on your forehead or arms by your side. Using your lower back muscles you slowly lift your torso off the floor - the height of this will depend on your strength. Don't use your arms to help. Hold at the top for a couple of seconds before lowering down. This movement can be increased on the hyperextension machine just be aware your hamstrings and glutes will be worked more as well.
There are many more but these are my top 5 for hitting certain areas. If you are ever in doubt any exercise that is a row or involves a pull of some kind will be working your back.