I have fabricated custom counter tops for customers, and have also installed the preformed counter tops with the attached back-splash. The main issue of concern, when cutting laminated counter tops, is the tendency for the laminate to chip or break in an undesirable way, which may ruin the results of your efforts. However, there are simple tricks that can be used to minimize or prevent chipping. Understanding how your cutting tool of choice functions is important, as the actual cutting direction of the blade should always be such that the teeth contact the laminate first, then continue into the wood. This can be accomplished by cutting from the underside of the counter top, thus allowing the brittle laminate to be adequately supported as the saw teeth remove the material being cut. If the counter top is cut from the top side (laminate side) the saw teeth tend to lift and separate the unsupported laminate from the wood, and being brittle; it chips in an uncontrolled fashion.
The saw blade of choice should have small teeth designed for cutting hard materials. Do not use a wood ripping blade, with large teeth, as this stresses the laminate by removing too much material with each cut.
If the counter top is attached to cabinets and cannot be removed for cutting, there may be no option but to cut from the top (laminated) side. The best way to do this, is to use a circular saw with a very fine-toothed blade, and a straight-edge guide to insure an accurate cut. Do not attempt to cut the laminate and the wood substrate of the counter in one single cut. Rather, set the saw depth so that the blade barely contacts the laminate. Carefully follow the guide with the saw, allowing the blade teeth to merely "score" the surface of the laminate. Then, set the blade depth a fraction lower, and repeat the guided cut. Continue this "incremental cut" approach until the laminate thickness is fully cut, and the blade teeth are contacting the wood below it. Now that the brittle laminate has been carefully cut (without chipping) the remaining wood can be cut with a single pass. However, it is a good idea to use more than one pass to cut the wood also, if you have the time and patience to do so. The wood can be safely cut with 3/8" depth increments, for perfect results.
It is important to support the counter top on "both" sides of the intended cut line, to prevent the laminate from damage due to movement of the scrap piece before the cut has been completed.
If you do not have a fine-toothed saw blade for your circular saw (and prefer not to purchase one either) it is possible to perform the initial incremental cutting of the laminate with a large toothed "rip" saw blade, by removing the blade and turning it around, and installing it backwards in the saw. In this way, the teeth are unable to "grab" the laminate in an aggressive fashion, and score the laminate instead. Again, small increments are required, for satisfactory results. Once the laminate has been severed, return the blade to its correct position, and proceed to cut the wood.
If cutting a preformed counter top with attached back-splash, from the top (laminated side) the back-splash will pose a problem, as the saw will not have sufficient cutting depth for the 90 degree angle of the back-splash. Therefore, use the circular saw to perform as much of the intended cut as possible (using a guide fashioned and clamped to the "good surface" of the counter, not the scrap side). Be sure to include a guide for the back-splash as well, and the two guides must be carefully aligned with each other to prevent "mis-matched" cutting lines and an unwanted notch in the final project. Once the laminate has been cut with the circular saw (as far as possible) proceed to cut the remaining laminate section with a Dremel Tool; using great care to follow the line. If your hands are not steady, or you are not skilled with a Dremel Tool, modify your guide with shim boards to prevent the Dremel cut from straying into the "good side" of laminate. Once the laminate has been cut down to the wood surface, the finishing wood-cut can be made with a fine-toothed hand saw and close, careful attention to avoid nicking the laminate edge.
I hope this helps those who may not be able to afford expensive tools for their intended project, but are willing to take the time to achieve good results anyway. Good luck!