Burn fat and gain muscle?

So I’m on my school’s track and field team as a long distance runner and I run cross country too, but I need to burn off some more fat and gain some muscle before track season officially starts. I’m unable to get a gym membership so that’s out of the question. I guess my real question is: What can I do at home as extra efficient workouts? Also, should I have a modified diet or drink protein shakes? It would be great to get as much stuff I could do as possible, Thanks =D