Apologies if you have done laminate work before, if not, warning: Unsolicited advice below
A glue spreader for the contact cement makes it go on much more evenly. Basically a piece of metal or plastic with v notches like used for laying tile. A place like Home Depot probably has one sized for vinyl flooring that would work. If you have a big blob of contact cement in one place it can cause the laminate to be a little high in that spot. Not a huge deal on an outfeed table, but ideally something you don't want. If the glue surface is super uneven it can interfere with the bond though.
Let the glue dry to tacky, where it won't come of the laminate if you touch your finger to it. Don't let it sit overnight if possible. If you have enough extra, practicing on scrap isn't a bad idea. FYI, laminate likes to slide under table saw fences. It also sends sharp little chips all over the place when you cut it. I've had a few imbed a little bit in my fingers. More of an annoyance than anything.
A bunch of 3/4" sticks laid across the substate (your plywood) will keep the laminate from touching prematurely. Too many sticks is better than not enough. You basically only have one shot; it is nearly impossible to remove after you get a good bond started. Make sure you have enough overlap on all edges.
Remove enough sticks in the center to touch the laminate to the substrate (make sure you don't twist it or knock it off center in the process) and either work from the center out, or start from the center and go to one side then the other. Remove enough sticks to go 6-9 inches maybe 12 at a time. Use your hand to flatten and smooth out the laminate taking care not to get any air bubbles. Work from the center out. After you get the initial bond with your hands, use the J roller starting in the middle and work your way out. Always start with the roller working away from the center; the idea is that you will be pushing any air bubbles out rather than in. After you get a good bond it is OK to just go back and forth.
After you get it all affixed, you'll want to trim the excess. The router bit will probably get full of adhesive a couple times and need to be cleaned off. If you need to touch up the edges you can use a medium to medium fine file.
This was long winded I admit, and in practice it is pretty easy to do, though some of the steps and reasons aren't always obvious. There are videos out there of varying quality. I'd recommend watching at least a few of them. Good Luck!