Lozzz,
Yep, skinny-fat. I sometimes peruse the success photos posted on this board, and see alot of people, who've lost alot of weight, without exercise (specifically, weight trainingi), and are basically smaller versions of their fatter selves. This is not what I want to achieve. Seems like it's happened to you, BUT the good news is, you can fix it. Heavy (for you) weight training and a good diet will help you recompose your body.
Galatia offered some very good advice, IMO, about starting out. I would suggest tracking your food for a few weeks so you can get an idea of how much P,C,F you're getting. For muscle gain, which is what you want, you need to keep your protein intake at 1-1.5g per pound of body weight, increase your calories, and add back carbs (specifically around your workouts).
Don't do too much cardio........it will compete with muscle gain. As Deb (Galatia) said, and Dodger, too, 3x a week, 20-30' is all you need, for heart health, and to keep the higher calories from being stored as fat.
Tell your traininer you want to add muscle. A full body routine, 3 times a week, alternating days to start. Free weights are best, IMO, but machines are ok, too, to start. Again, as Deb said, start with lighter weights/more reps, just for the first few workouts, so you can learn proper form. Then make it a point to try to do 2 or 3 sets per exercise, 6 to 10 reps per set, using a weight that will allow you to do so. Like, if you can do 12-15 reps, the weight is too light, and if you can only do 2 reps, the weight is too heavy.
Every workout, try to increase somewhere, either one more rep, or a bit of weight, etc.
This is all general stuff. If you are TRULY serious, and you are committed to doing it, you can have a fabulous body, and it doesn't take as long as you'd think. Visible results in 6 weeks, guaranteed,
A few good sites to visit:
www.stumptuous.com
www.beyondlowcarb.net
Good luck to you!