I'll try to add a bit of the stuff I've learned over the years.
Diet is far more effective than exercise in changing body fat levels. Despite all the complex stuff you will be bombarded with, it's really a matter of understanding your Total Daily Energy Expenditure (TDEE) which is a function of BMR x activity rate. There will be a calorie count that keeps your weight constant at your TDEE. To lose weight, eat 500kcals less, to gain weight eat 500kcals more. Varying by more than this can screw your metabolic rate around. You can increase your TDEE by exercising more of course.
Beware of falling into the cardio trap: Lots of aerobic exercise (or dropping your cals too far) which conditions your body to store fat. Storing muscle is "expensive" for the body in terms of calorie expenditure. So starve your body and it will drop muscle to survive, which therefore reduces your BMR & TDEE more, causing a reaction of reducing cals/exercising more: the cardio trap.
Lift weights: More Lean Body Mass increases your TDEE. Don't worry about getting "too big" there are a ton of people in the gym trying to get big so you won't do it by accident. If you do want to get big, you really need to eat higher than your TDEE so be prepared to gain a bit of fat in the process.
I haven't yet cracked how to maintain all strength whilst dropping body fat. I got below 10% but lost a bit of strength. I'm decent power-lifter strong now, but at 15%
