In order to make a shot of espresso without an espresso machine, use a cafetiere, Moka pot or Handpresso to brew the espresso beans. Espresso is made by water passing through coffee grounds at a high pressure, and this process can be emulated to a lesser extent with an alternative device.
A cafetiere is a machine that holds coffee grounds at the bottom, and the user pours almost boiling water over the grounds. After waiting the desired amount of time, the user pushes the plunger down, forcing the grounds to the bottom of the pot, and the coffee streams through the mesh to the top of the pot. More grounds and longer wait times lead to stronger coffee.
Moka pots are essentially stove top coffee makers, as they utilize a central basket to place the grounds and a bottom pot that holds the water. As the water is heated by the stove, the water temperature rises above boiling, allowing the water to extract more caffeine from the grounds.
A Handpresso is basically a manual espresso machine, so rather than using electricity and a machine to build pressure, the Handpresso relies on the user pumping the machine to raise the pressure to 16 times the atmospheric pressure. Because this gadget uses high pressure to extract the caffeine, the coffee produced is a shot of espresso.