Alright Hayden, it really depends on what you want to do.. I am trying to get SUPER fit to prepare for BUD/S ( Basic Underwater Demolition / SEALs, The SEAL training ) Things I do..
I don't diet, my eating is already healthy and always has been.. 3 Meals a day, nothing more.. ( Meal as in.. proper meal ) I snack sometimes in between, but nothing fatty or high on calories. As you said, You can't go to the gym, which I do 3 times a week.. So I suppose just do sets of pushups, pull ups and situps.. and run maybe.. 3 miles for the first two weeks, then increase to 4 or 5 on the 3rd or 4th week. ( Running is everyday ) Depending on your arm strength I find that the best thing to do is a set of 20 pushups, 40 situps, and then 5-10 pullups.. without stopping. ( Repeat that maybe.. 10 times, You can rest in between ) I also do dips ( Putting two chairs about 3 or 4 feet apart, holding your arms on the front chair and the legs on the back, and lowering and rising, along with the pushup/situp/pullup routine ) Of course, If you don't have anywhere to do pullups thats fine too. I go to the pool the 3 other days and swim 10 laps back and forth from one end to the other.. then rest a bit and practice my diving, I do half pool lengths of swimming underwater, 5 or 10 in a row, back and forth, with breath regeneration in between.. Then I ride my bike back home.. and I rest on Sundays

( This is my workout during the Summer, I do it every year, but the next 4 years this will be a year round workout.. )
Also, get a good pair of running shoes, and some comfortable clothes.. Sweat pants/ shirt are always good. ( I run in combat boots because I need to learn for SEAL training.. but I assume you don't really have access to those. )
If you want easier workouts, join a sports team.. they usually get you fit without you realizing

You can also go hiking / backpacking.. rock climbing, join marathons or triathlons..