The way to trade fat for muscle is to continually stress your muscles (by increasing the weight you can lift), and getting enough sleep (which I am bad at). Also, don't each too much (especially sugars).
+ Beginners: do air squats (multiple sets and repetitions) and static squats / wall sits (for as long as is comfortable. rest 90 seconds and repeat). Once you are stronger, do the same while holding a gallon of water.
+ Making Progress?: The above + yoga moves targeted at strength. Try out planks and wall hand stands. Single leg split squats (your back leg on your sofa).
+ Feeling Strong?: All of the above + adjustable kettlebells (let me know if you need recs) + gymnastic rings (you can attach the straps to a high place at a public park, or drill some hooks into your ceiling, or buy a doorway mount). Check out the bodyweightfitness community on reddit.
+ Advanced: This takes up space and costs a decent amount of $, but you'll need to build a home weightlifting gym with a barbell, olympic weight plates, and a squat stand / pullup bar / flat bench. Check out the homegym community on reddit.