I would agree with the 5/8ths if you can find it. I did some custom shelving and desks with double sided wilsonart laminate and it adds about 1/16th per side. So starting with 5/8ths you will end up really close to 3/4ths if you do both sides.
You want to use contact cement to attach it. Super easy to use, just get a can of the stuff at HD or Lowes, and some paint rollers (you want as thin of a nap on the rollers as you can get - 1/8in is ideal). You can search the web for instructions, but this is how I do it:
First cut wood to shape. Then rough cut laminate using a sharp utility knife. I score the cut line with about 4-5 passes using the knife on the good side of the laminate (good side up) and then while holding it down snap up to break on the line (if you snap down you will splinter the bad (glue) side). Wear gloves if you do it like that, cut laminate is sharp. You want the laminate to overhang your wood by at least an inch on all sides (I usually do a couple inches).
Using normal paint rolling technique, roll the contact cement onto the wood and the backside of the laminate. Wait for it to dry on both. To attach you lay the wood horizontal across some sawhorses or such, flip the laminate and stick. But you don't want to do it quite like that, when the two contact cements touch they will be stuck permanently, so I learned a great trick from someone on how to attach easily.
Get a long electrical power cord, like one of the long orange utility ones. Place it in a "S" shape back and forth across the wood on top of the dried contact cement. Flip the laminate so it is glue side down and place on top of the power cord. Position as needed then start at one side, pull the cord out a little bit, press down to attach, then go across the piece pulling the cord out and attaching as you go.
Once it is all stuck down use a 3in J-roller to roll it all over to make sure it's stuck well. Then get a router or laminate trimmer, with a flush trim bit, and trim the edge.