How to lose fat and build up muscle without losing weight?

Anonymous
I'm 117 lbs and 5'2 tall. I don't want to lose weight, I'd like to tone up my muscles (abs and legs) and to lose some fat (I could be defined as a "skinny fat").
What kind of exercise should I do? How often and for how long? What should I eat? (I'm vegetarian)
How to lose fat and build up muscle without losing weight?
3 Opinion