I used foam core board for the first time to frame my Home Sweet Home sampler.    I had fun distressing and glazing the frame, which I found in the thrift store.  It started out as glossy white.
Picture
frame and cloth are both distressed - they started out snowy white...
I bought a big panel (32" x 40") of foam core board at our local frame shop for under $7.  This board is made in 3 layers: card stock, foam, card stock.  It needs to be cut with a sharp utility knife in 3 passes, cutting one layer at a time.  I cut the board a little smaller than frame opening, so there would be room for the aida cloth.
Picture
use stainless steel pins to position the fabric to the foam board
The fabric can be centered quite easily and fastened in place by pushing stainless steel dressmaker pins in place along the side of the foam board, as I pictured.  The pins stay in too.

The next step is to miter the fabric on the back, by folding in the excess aida cloth and stitching the sides together.  (I didn't want to cut the excess cloth off, in case I decide to display it differently later on.) 

I stitched the corners together in two steps:  starting at the outside and then finishing the inside after I wove the sides together.  Some people skip the weaving altogether, as the pins hold the cloth very securely.
Picture
back is mitered and woven together
After that, you are ready to pop the fabric covered board right in the frame and proceed to display.  I don't like to use glass with needlework, but that's just me.
Picture
I'm ready to frame - that really wasn't so bad!