I'll run through how I attach removable panels using this method.
Ok, so you need a panel that you will be attaching and a panel that will be attached to (I'll be using foam core board in this demonstration). You'll also need a roll of tape. I typically use clear packing tape, but this should work with whatever tape you have. A good thing to do at this point is to position the removable panel down on the background panel. Get it right where you want it and lightly mark the corners with a pencil. These registration marks will help later.
First, pull off a piece of tape and attach it to the panel you will be attaching. If this were a large sign, I would do this in each corner.
Pull off a piece of tape and roll it into a loop so that the sticky side faces out. Then stick it down in the center of the piece of tape you already stuck down. Flatten the loop down.
Pull off a piece of tape roughly the same size as the first piece you stuck down. Stick the tape (sticky side up) onto the loop of tape. So at this point you should have three layers of tape (sticky side down, loop, sticky side up).
Pick up the panel and carefully line up and push down the taped side to the background panel using the registration marks you made earlier.