Building muscle requires brain power and creativity.
Many people make the mistake of thinking they need to have the heaviest weights possible in order to build muscle. In truth, if you shift your mental & muscle focus towards the muscle itself and not the weight, you can build muscle. You need to establish the Mind + Muscle connection.
Do you have access to a pen or pencil?
Hold one in your hand and hold it with muscles clenched for 2 minutes. Give it a try.
Do you have a chair?
Hold it like a barbell. Pick it up, curl it and set it down.
Do you have a textbook or access to a library?
Hold your hands with your palms facing upwards. Place a book in each hand. Clench your muscles and hold that pose for as long as you can.
Do you have any canned goods? Or a bottle of water, soda or a beverage?
Sit in a chair, hold them in your hand with muscles clenched and do concentration curls with them.
Do you have a floor?
Do some pushups and explore the different hand positions/angles that target your biceps and triceps.
Do you have a wall?
Do wall squats. If you want big arms you need to work your quads.
Do you have a pull up bar at home or in a park in your city?
Do underhand grip front-facing pullups. This builds your back AND your biceps.
Do you have a $5 jump rope?
Jump rope to target your quads and keep those arms moving.
Is there a community garden or a field of dirt near you?
Grab a shovel and spend 45 minutes doing some fast, hard shoveling. You will definitely feel it.
Your takeaway: you do not need a gym membership to build muscle. Ever.