If you have carefully fitted a new piece to another that is already in place, you must be careful it does not move, as once the contact cement bonds you can't move it. Let's say you're working on a counter top. Make sure you have fresh air.
Cut craft paper or ordinary wax paper into strips that you can lay on the counter top, letting them stick over the edge to be pulled out as you go along. Wax paper off the roll is only a foot wide, that's okay for width. If the strips are too wide they are hard to pull out.
Mark the edges where they join to avoid a mistake, then coat both surfaces with contact cement and let it become dry to the touch. Arrange the wax paper to cover the counter top, and then carefully set the new piece in place, making sure the joint is butted exactly tight. It's best to have a helper hold this firmly while you remove the wax paper from under the other end of the Formica and press well down on a few inch of the end to make good contact, this ensures the new piece can't move.
You can now proceed to carefully remove the rest of the wax paper; lift the new piece a wee bit to make sure the paper will pull out and not tear, as a small piece caught between, prevents that part from sticking. Make very sure the joint has fallen perfectly into place "before" you start pressing the new piece down; if the edge of the new piece doesn't want to go down, and this does sometime happen, you can still carefully nudge it down. Remember: if you have firmly stuck the other end down so it can't move, so you should be okay.
So it's in place. The joint looks good; now make a towel into a ball; push down on it hard as you rub down the new piece, all over, back and forth. That's it except dressing the front edge if necessary, and cleaning off any cement.