Cover plate dies and lining up the pieces.

Are you saying the background is plaid and you want to make sure the paper you cut with the die lines up with it? If so, I use liquid glue so there is time to move it around if I need to. If that is not what you meant, I'm confused about your question, so ignore me.

ETA: OR... If you have a stamp platform for even a scoreboard you can butt the bottom to the corner and then do the same with the die cut one. But often for me that doesn't work so good. 

I'm assuming you are doing the inlay technique so I was going to say liquid glue too.  And using a pick up tool to easily nestle your piece in place.

If you’re doing the inlay technique this is how I would do it.  Make your sandwich; cutting plate, paper, die, top plate but flip it over to run through the die cutter. Remove the top plate, put a piece of press n seal over the whole thing, put the plate back on top then flip again. Remove the die, carefully peel the outline piece off and all the little pieces should remain stuck to the press n seal in the proper order. Use your pick tool to hold those little pieces in place as you peel the large piece off.