I either drape it over my sewing chair, or across my sewing machine table. I have a separate table for cutting. Right next to the cutting table is a couch, so it gets used constantly for holding quilting stuff.

I also have 2 other nice computer chairs (same as my sewing chair) that sometimes get appropriated for use.

I installed a towel rack next to my ironing board in my sewing room. I just hang my ironed fabric right over it. Works great!

I have one of those wooden laundry drying racks( little wooden dowels) That folds flat when your done with it. I use it in my sewing room all the time.

When I audition fabric for a new quilt, I iron the ones that I will be using and lay them over the back of the chair or on a small table that is directly next to the iron.

I iron it all, with fabrics on the bed as need be, then take it all to the cutting board (in another room) and cut. The cutting area is large enough for fabric piles off to the side of the cutting board.

I iron and cut one piece at a time. I don't have the patience to iron it all first. :)

I usually do the same as Dunster. If I need to have more than one fabric ironed at the same time, I use pants/skirt hangars and hang in the closet until needed. Sometimes I'd rather iron than sew and this method works for me.

I figure out how much I want to cut first. Then I Best Press and then cut the strips/pieces that fit in that amount of fabric. I do NOT do the whole thing at once but in increments.
A friend explained how she doesn't get tired of making quilts when she can vary what she is working on. She limits herself to cutting no more than 5 blocks at a time, then chain sewing as she makes the blocks, etc.

Im the starch and cut as I go along brigade, if I have any long pieces I.e. borders I'm not using right away I hang over the bannister on the top hallway over the stairs.

Thank you everyone for all the ideas. I've decided to invest in a second ironing board for my cut fabric. It's smaller than a table (which I definitely don't have room for) and it will fold up out of the way when I don't need two ironing boards.