dealing with foam

Right glue is Elmer's white glue.

If you are talking styrofam, I use tow or three types.
(i) White glue - PVA - works pretty well for things like laminating slabs together, and at a pinch can be used for skinning if you can ke[p an even pressure on teh whole shebang for a few hours. PVA is ideal for skinning with paper - tissue or brown.
(ii) General work of joining other things to it I tend to use epoxy. If you mix this with microballons its a lot lighter, and still stronger then the foam anyway.
(iii) I have experimented with contact adhesives - there is a rubbery adhesive (Copydex?) that smells of amonnia, and is often used to stick fabrc to wood etc. It works - or can work - as a contact glue, and so is useful for rapid skinning of the stuff.
(iv) I haven't used it, but there are some water based polyurethane glues out there that allegeldly work well also.
MOST CA's attack the stuff badly. As do most solvent based glues.

"Hold the Foam" from a crafts store Instant Grab, Repositionable, water cleanup.