I would recommend the book "Never Gymless" for someone in your situation, imo it is the resource for training without equipment. It has 100s of equipment free exercises for building all aspects of fitness including strength. Some of the exercises are listed below.
Strength Exercises: Pushups, Diamond Pushups, Clapping Pushups, One handed Pushups, Pike Presses, Hand Stand Pushups, Calf Raises, Squats, One legged squats, Squat jumps, Pullups, Muscle ups.
Core Exercises: Planks, L-sits, chinnies, ab wheel roll out (I know it's equipment but very cheap), dragon flag raises.
Conditioning Exercises: Running, Skipping, Burpees
Program creation based on your goals is also covered in the book and a very important part of training. Anyone can exercise but the difference between training and exercise is having a specific goal and tailoring your exercise routine to attain that goal.