How to make cappuccino coffee at home without a machine
Do you have a French press? If so, you can make coffee that is quite strong in there and you can froth your milk. 

For the coffee, grind it course. If it's too fine, too much will go through the mesh and your coffee will be murky and over extracted. Buy a very dark roast, but something that isn't too smoky. Italian roast is too smoky. Espresso beans typically have more of a caramelized flavor vs. smoky. 

For the milk, warm it a little more than you want for your cappuccino. Put it in the clean press. Vigorously pump the plunger up and down. This will make luscious, dense foam. If there are too many large bubbles pump longer, or you can stir it a little. 

I don't love specialized or expensive equipment either. French presses are inexpensive and useful for steeping many things. They are also small, and you can use them when you are away from electricity (camping/zombie apocalypse/etc).