Staying Gluten Free is going to be priority number and shopping is gonna be your one way to control what you put in and around your body. So the number one advice to take plenty of time, and not to rush. Therefore its a good idea to go to the store during off peak hours. Also make sure you create a list beforehand to help save some time.

Here are a list of items to get familiar with and read when picking up ANY packaged or canned food, regardless if you have purchased it before! 

Other text on labels to look for:
‘manufactured in a facility that also… and ALWAYS AVOID ’made on the same lines as wheat, barley (etc)…’

But most importantly look for the following:

Abyssinian Hard (Wheat triticum durum)
Amp-Isostearoyl Hydrolyzed Wheat Protein
Atta Flour
Barley Grass (can contain seeds)
Barley Hordeum vulgare
Barley Malt
Beer (most contain barley or wheat)
Bleached Flour
Bran
Flour
Brewer’s Yeast
Brown Flour
Bulgur (Bulgar Wheat/Nuts)
Bulgur Wheat
Cereal Binding
Chilton
Club Wheat (Triticum aestivum subspecies compactum)
Common Wheat (Triticum aestivum)
Crumbs
Cookie Dough
Cookie Dough Pieces
Couscous
Criped Rice
Dinkle (Spelt)
Disodium Wheatgermamido Peg-2 Sulfosuccinate
Durum wheat (Triticum durum)
Edible Coatings
Edible Films
Edible Starch
Einkorn (Triticum monococcum)
Emmer (Triticum dicoccon)
Enriched Bleached Flour
Enriched Bleached Wheat Flour
Enriched Flour
Farina
Farina Graham
Farro
Filler
Flour (normally this is wheat)
Fu (dried wheat gluten)
Germ
Graham Flour
Granary Flour
Groats (barley, wheat)
Hard Wheat
Heeng
Hing
Hordeum Vulgare Extract
Hydrolyzed Wheat Gluten
Hydrolyzed Wheat Protein
Hydrolyzed Wheat Protein Pg-Propyl Silanetriol
Hydrolyzed Wheat Starch
Hydroxypropyltrimonium Hydrolyzed Wheat Protein
Kamut wheat)
Kecap Manis
Soy Sauce
Ketjap Manis (Soy Sauce)
Kluski Pasta
Maida (Indian wheat flour)
Malt
Malted Barley Flour
Malted Milk
Malt Extract
Malt Syrup
Malt Flavoring
Malt Vinegar
Macha Wheat (Triticum aestivum)
Matza
Matzah
Matzo
Matzo Semolina
Meringue
Meripro 711
Mir
Nishasta
Oriental Wheat (Triticum turanicum)
Orzo Pasta
Pasta
Pearl Barley
Persian Wheat (Triticum carthlicum)
Perungayam
Poulard Wheat (Triticum turgidum)
Polish Wheat (Triticum polonicum)
Rice Malt (if barley or Koji are used)
Roux
Rusk
Rye
Seitan
Semolina
Semolina Triticum
Shot Wheat (Triticum aestivum) 
Small Spelt
Spirits (Specific Types)
Spelt (Triticum spelta)
Sprouted Wheat or Barley
Stearyldimoniumhydroxypropyl Hydrolyzed Wheat Protein
Strong Flour
Suet in Packets
Tabbouleh
Tabouli
Teriyaki Sauce
Timopheevi Wheat (Triticum timopheevii)
Triticale X triticosecale
Triticum Vulgare (Wheat) Flour Lipids
Triticum Vulgare (Wheat) Germ Extract
Triticum Vulgare (Wheat) Germ Oil
Udon (wheat noodles Unbleached Flour
Vavilovi Wheat (Triticum aestivum)
Vital Wheat Gluten
Wheat, Abyssinian Hard triticum durum
Wheat amino acids
Wheat Bran Extract
Wheat, Bulgur
Wheat Durum Triticum
Wheat Germ Extract
Wheat Germ Glycerides
Wheat Germ Oil
Wheat Germamidopropyldimonium Hydroxypropyl Hydrolyzed Wheat Protein
Wheat Grass (can contain seeds)
Wheat Nuts
Wheat Protein
Wheat Triticum aestivum
Wheat Triticum Monococcum
Wheat (Triticum Vulgare) Bran Extract
Whole- Flour
Wild Einkorn (Triticum boeotictim)
Wild Emmer (Triticum dicoccoides)

Source of awesome food can labels you can print out for yourself:

http://blastr.com/pics/BruceCampbellsSoupLabels-scifiwire.pdf

 

Here is an example of other fun print outs you can get on the web to help with food label conundrums:

http://cdn.glutenfreely.com/pdf/Gluten_Free_Products.pdf