Hello Racheal and welcome to the Community.
As Adam444 stated a small router is used to cut laminate after it has been applied.
Contact cement is use to install laminate to smooth clean particaI board. I fear you may have a problem applying laminate over a painted surface. The contact cement may break down the paint, causing it to bubble or deteriorate. As a result the compromise the adhesion of the laminate.
Try applying contact cement to a small inconspicuous spot to see how it reacts. If you choose to attempt this, you may want to try to strip the paint first. Laminate manufactures may not warranty this application.
Formica one of the suppliers of laminate to the Home Depot, has an excellent web site that can provide a great deal of information about laminate and how they are applied along with many videos.
If you are interested replacing the complete counter top, each Home Depot employs a very knownlegible Kitchen design staff that would be more than happy to assist you. Click here for the In-store Appointment Maker.
Thanks for your inquiry.