WARNING - anal foam post iminent!
The issue with various rigid foams (styrofoam/styrodur and the various insulation foams) is that the actual density of the individual foam, along with its cell size, will actually dictate to what extent you can use various paints/coverings succesfully on it - it can also change the effect of various glues.
I mention all this as way of explaining why you will get a wide variety of answer on using spray paints succesfully ( or not) and how some people may say one glue works whilst another says it wont.
"pink" foams are usually arouns 20-30kg/m3 (they vary by brand) and have a bigger cell structure and are more susceptible to spray paints (or the accelerants in it I should say). They will work better with PVA or other air-dry glues as the open cell structure allows breathing for the glue to set.
At the other end of the spectrum are super-dense foams of 200kg/m3 which are used to make industrial blanks, surfboards and windsurfaers - this stuff is pretty indestructible.
Inbetween are the "blue" foams - normally Styrofoam and Styrodur (both brand names - note the capital S) which go from about 32kg/m3 up to about 52kg/m3. The high 52kg/m3 is smooth-styrofoam with a tiny cell structure, smooth texture and which you can even use superglues on with success without melting. 40kg/m3 and 32kg/m3 (which are the usually european weights for insulation styrofoam such as "Floormate 200-X" and "Styrofoam LB" will be melted by superglues but may not allow air-drying glues to dry properly ( so use UHU Por or Foam-2-foam) for gluing them.
And just to make things really awkward: the colour of the various foams is now largely irrelevant to actual properties. The colours were orignally developed over time with manufacturers trying to indicate their own brand type by a colour e.g. Styrofoam (brand name) was always blue. Unfortunately this no longer works acurately as you will find lightweight blue foams and heavyweight pink ones - there are now also green foams, red foams and yellow foams all in the 30-42kg/m3 ranges e.g you can now get Styrofoam (brandname) in green.
There are some general rules of thumb though (and for this when i say "styrofoam" i mean all rigid foam not just the brand Styrofoam):
"proper" glues that you can guarentee will stick sheets together are: UHU Por (contact adhesive with high strength contact grab, sandable) and Foam-2-Foam (long setting time, allows repositioning but actually foams the best seal over a 8 hour set time). Both of those types are UK/Euro available - sorry but i don't know the north american or pacific brandnames.
For covering you are safe to bet on any latex-acrylic paint. IN UK/Europe these are generally types such as masonry exterior paints such as Dulux Weathershield... but any latex-acrylic paint will grab styrofoam without an undercoat needed, it wont melt any styrofoam (or even expanded polystyrene) and has some inate flexibility that works well with the flexibility in the foam itself.
On the simple premise that unless you know the exact density of your particular foam AND you know the exact propellant of a spray paint - DONT use any spray paint on a foam even if it says it is "ok for use on styrofoam" - because what they call styrofoam might not be what you ahve been sold as styrofoam.
Thus: always test a small section by spraying an offcut up close with the spray paint. Doing it upclose ensure you hit the foam with a good dollop of propellant - if it doesnt melt then it never will.
And, just to give an idea of the variations out there - we have access to 72 different types (brandnames) of "styrofoam" within the UK only - ALL of which are fine for modelling with, depending on final use... but many of which act entirely differently to the others.
If you've read this far though at least you will now know why you see so many varied replies and results using various spray paints and glues: "sytrofoam" is not always "Styrofoam".