Basically, you need to make a play clip brush, the size of the model of the door you want to make. Make that brush into a func_foor, and set the direction you want it to move in, also set a meaningful name. Next make a prop_dynamic, with the model of the door, and set the parent to the playerclip brush.
Make sure you set the flags on the door to not open on use or touch, but when the input is triggered it will open.
Put the model inside the playerclip brush, and now from any other entity output, you can call the door to open.