Open the epoxy paste containers. You will have to mix two or more parts -- commonly labeled A and B -- to create the epoxy. Follow the mixing instructions on the manufacturer label. Pour the A and B parts into a clean mixing container. Insert a stiff putty knife into the final paste and stir it up.
Fill a caulk gun with the epoxy paste. Hold the caulk gun at the handle and position the gun's nozzle over the area that you are caulking. Press the trigger to release the epoxy paste through the nozzle. Move your arm in the direction of the line that you must seal or bind, making the caulk gun follow. Keep an even line of the caulk -- referred to as a bead -- so that you don't create gaps in the seal.
Smooth the surface of the epoxy paste with the putty knife, if you added too much and need to flatten it out.
Note the hardening time for the epoxy paste. This is based on the temperature in the room. For instance, according to The Family Handyman, if you're working in a 70-degree temperature, the epoxy begins to harden in approximately 30 minutes. The hotter the temperature, the faster the epoxy hardens. As such, it is better to work in cooler environments so you have a longer amount of time to perfect the caulking with the epoxy paste.