Hi, I have had a lot of experience with this. There are basically two ways to go if you don't want to have your counters completely re-done from scratch. For both of these you really should remove your sink and the entire counter from the top of the cabinets. This sounds like a lot, but the plumbing all unscrews and the sink (if a standard stainless steel one) is only held on by clips along the under side and by calking. The counter is usually only held on by a few screws going up from the base cabinet corner braces. Even if it was glued down, you should be able to cut through this with a utility knife. Note: It is possible, but not likely, that your counter substrate was built in place and is not easily removed as described above.
The two methods are: Removing the laminate and keeping it and going over it.
Method one: Removing the laminate. The one mortal enemy of contact cement is heat. I discovered this when I fired up my shop's wood stove one day and found that some counter sink cutouts, which had laminate on them, were delaminating from the heat. I walked over and just peeled the laminate right off. You could achieve similar results with a standard heat gun. Do not get it too hot or it could catch on fire. Have a fire extinguisher handy just in case and do this only in a well ventilated area in case there are any fumes. The end result should be clean counters without laminate. Put new contact cement on the substrate and the laminate and proceed as a normal new counter. Note: all of this only applies if the condition of the existing substrate is very good, ie: no swelling from water etc. My other trick is that I ALWAYS use two coats of contact cement on both the substrate and the laminate. Once the first coat crazes over (15 minutes) then I put on another. I have never had a loose laminate install.
Method 2. putting new laminate on over the old stuff. This is riskier. You need to tap the entire surface with your finger, listening for loose spots. If you think there is any delamination then remove the laminate. If you have a beveled edge then you should just get a whole new counter made because you won't be able to figure out an edge detail. If you are confident in the existing laminates attachment, then you should scuff up the entire surface with 80 grit sandpaper, being sure not to miss any spots. Then apply your two coats of contact cement and proceed as a normal laminate install. Good luck!