The standard press to hold SIPS (house) panels together is pneumatic, it's not hydraulic and does not need vast amounts of pressure. It's important that the surfaces bond during the curing phase of the glue.
http://siptec.co.uk/wp-content/uploads/2012/03/SIPs-In-Press.jpgThere are two glues used with polystyrene SIPs panels in the UK, PU (multipart polyurethane) and cross linked external PVA. (Cross linked means when it's cured it does not turn back into mush if it gets wet.) The test for a sips panel bond is a tear test: pull the two sheets apart and the polystyrene should tear and not tear along the glue line. The glue needs to be just stronger than polystyrene. It's worth doing a few small trial tests with your materials. Most
external pva wood glues are crosslinked for obvious reasons.
https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcRGEQes6Uq-CwzLez_47bYCb5LCfqELIRLjFxgK4jOqWdYgltTcThis link shows a SIPS glue spreader and laying up a press.
http://www.fischersips.com/our-projects/commercial-projects/week-1From a DIY point of view, the PVA glue can be applied with a paint roller to the lower skin, you don't need lots, it just needs to look white as if it's been painted. Check that the polystyrene is the same thickness for each panel (uniform bond). The polystyrene and stud put into position, more glue painted on to the polystyrene and the top skin put into position. It is ideal to stack multiple layers of panels directly on top of each other: normally full sheet blank panels are made up and then cut into shape. If there are big holes (windows/doors) in the panels then you will need to fill these with "fillers" to transfer the pressure all the way through the stack. Be careful not to move the lower panels when laying up the upper sips panels: use a wall or straight edge as a register. With something like an 18mm ply, put this (unglued) onto the top skin and load it up with weights trying to keep the load uniform across the panel. 5 or 10 gallon containers filled with water would work pretty well. Let the glue cure, if it cold it may take a day or so longer.
The process is simple. The reason why this DIY method is not done for house building, is it's a bit Heath Robinson, the glue spreading is inconsistent, there is no warranties and you can't get a mortgage if you are building a house.
The usual caveats, common sense and legal jargon and get out clauses apply.