How to "mount" acoustic foam ?


My main system is in my partially unfinished basement.
While I have finished the ceiling and have nice floors / rugs - I do like the industrial / rough look of the concrete walls....I just finished painting them but don't want to install any sheetrock / finishing material.
Instead I want to buy acoustic foam (2inch depth squares) and mount them to the walls - front / back and sides
And here are my questions:
1. Should I just use glue and apply the foam squares directly to the wall ?
 - IF YES - what glue should I use? I know there is the special construction glue for laying floors etc..... I now they sell it also for concrete and stone application - sold in caulk like tubes 
2. Should I first apply the foam  to a plywood / wood and anchor that to the floors ?
 - IF YES - I would imagine a few concerns: 
-  Will that wooden structure bring about sound resonance that I am actually trying to control ? (Wood isn't as bad as concrete but still....) 
-  Will I have to add a layer of caulk or similar filler between the wall and  the wooden panel? Obviously the concrete walls are not super smooth so the wood panels will not be in perfect and uniform contact. They will be held rigid with the specialty screws drilled into the walls....but still 
- What type of panels should I use....I was thinking anything from very thin cardboard like materials (to minimize any resonance from wood) to 1/2 inch plywood for rigidity.
IN SUMMARY: 

 I am leaning for the 1/8inch thick boards - In my mind it would provide smooth surface to mount the foam onto, retain the acoustic profile of the foam, and then just hold it all in place up on the wall with 4 bolts (each corner)

Anyhow....Any other tips and advice about proper installation would be appreciated.

Thank you!! 
ether
A good place to start is a clap test to see if you have an echo. You can tame the echo by using what you suggested above with the foam & 1/8" boards. Try to locate them near the 1st dispersion bounce points which would be the surfaces closest to where theoretically the tweeter & mid-range meet a surface (wall, ceiling, floor). That would be 180 degrees for a dome tweeter. If you have bass issues, maybe a pair of bass traps in the corners behind the speakers. Also, I use triangle corner tunes in the upper corners of the room. I would also get your ProAc's out into the room so that the speakers are 1/3 out from the rear wall, 1/3 from your listening chair and the chair 1/3 from the rear wall.
Using Auralex 2" Studiofoam and LENRDs in my listening room.  Back wall, from the ceiling to one foot below my ear level.    The room overloaded quickly, without the stuff, at my typical listening levels.   I found latex construction adhesive, to work well(been hanging there for the past 20+ years).  
@ether the point @geoffkait is making is that any amount of acoustic foam is audible and deleterious.

I have a fully treated room with tube traps and diffusion along with a range of SR treatments. I was using small (6”x12”) bits of foam to break up reflections from the edges of my components. As soon as I took these out I realized they create a harsh and edgy timbre.  

Please don’t use any foam in your room. Treatments from GIK are quite cheap (I ended up with a pair of custom GOBOs to address my component stack issues) and will sound so much better. Even natural rugs or wall hangings will be better than synthetic foam
But seriously, acoustic foam is one of the biggest scams ever perpetrated on naive and gullible audiophiles.

FALSE!

We’ve already gone over this in at least one other thread. Consider that GIK Acoustics acknowledges that 4 inches of acoustic foam panels equates to 1 inch of their fiberglass (and other materials) product.

Any other tips and advice about proper installation would be appreciated.

OP, I use foam acoustic panels, albeit not on concrete http://halr.x10.mx/AV.jpg

In my case they are mounted three different ways. Bass traps in the corners were adhered with a 3M spray glue. Wall panels were adhered with a 3M velcro strip. The ceiling panels were installed with (less than desirable and very few) carpet tacks.

Try the velcro strips in your case.
Perhaps you haven’t heard Melamine acoustic foam, SONEX or foam that looks like SONEX. I acknowledge there might be some kind of foam that doesn’t hurt the sound, I just never heard one is all. Fiberglass is not foam, obviously. Hey, I’m not trying to disparage all acoustic panels. For slap echo Michael Green’s Echo Tunes work great. But SONEX Melamine foam or similar foams - like the foam in Ikea chairs, for example - do actually suck, making the sound phasey and wooly sounding. I can even hear the effect of SONEX when I take it to another room. Ikea chairs - another sonic catastrophe that seems like such a good idea. “SONEX, trusted by professional studios everywhere.” 😛

One final thought: acoustic panels and Echo Tunes and Tube Traps and really all acoustic devices, even tiny little bowls, are trickier than they appear to correctly set up or apply. What is needed is the out of phase track on the XLO CD. The same track used for finding the absolute best speaker locations, which of course change as you apply more and more room acoustic treatment. It’s a fluid situation. Everything is in flux. Been there done that. 😬