I can get a special laminate cleaning fluid here in Germany. There is quite a choice actually. My favourite is an eco-friendly one which smells of orange.
I NEVER use the vacuum cleaner on it. Too much hassle, to noisy. I use the mops with microfibre or other light material covers, and wash them after each use. You can pick up a pack of 2 in pound shops so I have several.
I half fill a bucket with very hot water and a squirt of the laminate cleaner, dip the mop-head in and wring it out really tightly. The mop is wider than a vaccum cleaner head so you're done quicker.
Wipe around (without lifting the mop). Do not rinse or rub dry as this takes away the shine.
If there are lots of bits, e.g. fluff, dirt, crumbs on the floor, you can sweep them up first using the dry mop. I find this gets more than a vacuum cleaner would and you can listen to the radio while you're doing it!