Just to add my 2p..
I think the original question was to lose weight and get fitter/stronger at the same time. Most of the advice seems to be around the strength/fitness aspect. Diet is vitally important too, as gdb19 mentioned.
Your body works on a thermodynamic basis - for conservation of weight, energy in must equal energy out. If the equation is imbalanced in either direction you will either lose or gain weight.
If you want to adjust your weight then, as gdb19 says, download myfitnesspal, plug in your details and log your eating habits. The app works out your total daily energy expenditure (TDEE) and then tells you how much you should eat to reach whatever weight you want to. So, for example, if you want to lose 1lb / 0.5kg per week, you should eat 500 calories under your TDEE per day. Most sources seem to agree that in order to lose 1lb of weight, you should eat 3500 calories under your weekly calorie requirement.
Obviously you don't have to use myfitnesspal, you can count calories yourself, but it does make it easier. There's also this:
http://www.1percentedge.com/ifcalc/ which is a more detailed calculator used if you want to get involved with intermittent fasting (IF). It's useful as it shows your basal metabolic rate (BMR) - which is basically the amount of calories you need to stay alive - and tells you how much you should eat on workout days as well as non-workout days.
Losing weight in a practical sense is actually pretty simple. It's the mental side that's a little more complicated!