first off, congrats on the weight loss!
a good way to build stamina is just to jog. start off jogging 0.50 miles every day for 7 days straight...then on monday of the new week bump it up to 0.60 miles every day...then next monday bump it up to 0.70 miles...etc etc etc....this is easier to do at a gym because you can keep track of it on the treadmill...this is how i was doing it for months until i got up to running about 2 and a half miles.
back in the day, i used the same method but used to jog on the levy by the river...instead of adding 0.10 miles every week, i would look at objects in the distance and would be like "ok, next week jog to there" (there being an end of a fence, or a tree, of a fire hydrant...anything that was a little bit farther from the previous week)
^but remember, this is all cardio...and is great for stamina....but for overall health (including muscle and bone strength) you need to do some resistance training.
no weights? no problem. stick with calisthenics...push ups, pull ups, squats without weights etc etc...doing burpees would be a good place to start (youtube the different types of burpees)..start off doing as many of these exercises as possible and just add to them every week...they will get easier to do.
google the onehundredpushups website....that actually helped me triple the amount of pushups i was doing....also, look into the convict conditioning book casek posted in here a while back (hopefully the link still works)
good luck, and let us know how its coming along!