take the sponge and fill it with water -
making sure that the sponge has a decent amount of water but is not dripping water when you hold it in the air -
lay two (in this case) sheets of the paper - two because this is 270 gsm paper - if the paper is lighter, say 180 to 200 gsm you might want to put three sheets at a time, and if lighter still, four or even five (which I have done for 120 gsm papers) -
drag, lightly, the damped sponge across the paper, making sure that the whole is evenly wet - Lewis Allen says no deserts or lakes - then lay another two sheets on top - damp those, then lay another two sheets down, damp those, and so on till the pile is completed - I tend to have at least one dry sheet on top - it may take a little experience to know how much water you should spread on the sheets - too much, and the ink will go fuzzy in printing - too little, and it will look as if the print is under-inked - it's all about the feel of things - some papers are more water-absorbent than others and buckle like crazy when water touches them - after a while you'll be able to guess what a particular paper needs - but nevertheless, be alert to the possibility of being surprised. . .
when you are thru the pile of sheets, place the second board on the top of the pile -
then wet the two towels (one may well be enough but I use two - and lay them over the pile of boards & paper -
when that's done, my stack looks like this -
I tend, following Lewis Allen in his Printing with the Handpress, to damp paper in the morning, let it stand all that day and the following night, to print the following morning - unlike Allen, I don't put weights on the stack (I used to, but found thru experiment that it wasn't necessary - he also recommended turning the stack over at day's end, and I'd also recommend that if you have 100 or more sheets in the pile - but I found it's not so necessary when I have 50 or so sheets - the result should not be wet sheets, almost not even 'damp' but just slightly cool to the touch - other printers have more elaborate processes than mine - but I've been using this method for over 20 years and it has always worked well for me