When working with plastic laminate, like Arborite and Formica, the material is rather thick, so trimming off the excess requires the use of power tools.
Whether using a small specialized laminate trimming tool or an ordinary router, the key is in the bits.
The edge trim should be completed first, before any glue is applied to the face of the board. This is because we will be creating dust that would foul the exposed glue on the surface. And we need that surface as a clean guide for the trimming tool. In addition, the edge has to be done first, so the face laminate can overlap the edge trim. This prevents you from catching it during normal use of the board and pulling off the edge trim, as is so common with melamine tape.
First, a little tip for permanent adhesion. Always prime the edge of the board with a layer of contact cement which you let dry for several hours if not overnight. Most of this glue will soak into the particle board or plywood edge leaving only a suggestion of glue. By letting it cure completely, it will form a very good base or prime coat for the real adhesion coat. If you do not prime the edge, there will be very little glue available to adhere to the laminate, which is why edge trim often comes loose.
Second apply contact cement to both the edge and the trim piece, wait for it to get tacky and then put them together, using a block of wood or a roller to press the trim into good contact.
Work around the board technique
To get four pieces of trim on a single board all at once without careful length measurements, start the first piece flush on one end but hanging out over the other end. Then butt in the second piece to the overhang, letting it overhang it's other end. Keep working your way around the board. All four edges can be put on with one end butted and the other overhanging, you don't have to do 2 edges then dress them before doing the other two edges.
The straight bit
Now we trim off this edge piece with a ball bearing guided straight bit that will cut the plastic flush and square with the face of the board. You will probably have to go back and remove some glue bumps and pass the router a second time to get this absolutely flat. Do not round this edge over. The face or surface piece is put on with a bit of overhang all around for easy alignment. You do not need to prime the face because this surface does not drink the contact cement like the edge of the board does.
The tapered bit
The surface or face laminate is not trimmed with the same straight bit used for the edges. There is a special tapered and ball bearing guided bit for this job.
You have to experiment on the depth adjustment of this bit. If it sticks out too little from the base of the router, it will not trim off the face laminate flush with the edge laminate. As you move it further and further out, the bevel cut will cause it to cut further and further into the board. If you stick it out too far, it will not only cut off the surface overhang, but will cut into the edge trim, with bad looking results. You want to adjust this bit so that it just barely cuts into the edge trim. This will leave a very neat little line, almost invisible, in the edge trim, a clean bevelled cut on the edge of the surface laminate that is all so slightly recessed back from the edge and the end result is an corner that is not sharp to the touch, hence you do not need to break the corner with sandpaper. If you were to cut the surface laminate with a straight bit you would have to go back and soften the edge by hand and you could easily find some places where there was an overhanging lip that you could catch and pull up on the surface laminate.
keep the bearing free of glue
One working problem with this bevled bit is that the ball bearing is always very close to the glue line, which tends to allow glue to accumulate between the ball bearing and the rest of the cutter. If you do not clean this occasionally (simply spray it with solvent and spin the bearing a bit) you will find the ball bearing seizing up and causing a burn mark on the edge trim.
So the key to laminate work is to buy a "pair" of laminate trimming bits, one straight and one bevelled.