My daughter is hypothyroid and follows a gluten free diet which she finds helps. There seems to be enough evidence to support her decisions.
You need to do your research and find out which foods are naturally gluten free first of all, then build your menus around these.
If you look on the ingredients list on most packets they will have known allergens in bold. You can obviously ignore most of those, but look and it will be clear which ones are best avoided.
Then as Annie says there is a huge selection in supermarkets these days, look for the 'Free From' shelves, but still read the labels and check it says GF free. There's everything from GF bread (horrid) cakes (yummy) cereals and muesli (can't tell the difference) pasta, stuffing mix, bread crumbs, pastry (chill counter) etc.
Worth knowing that cornflour is GF (I use it as a thickener) if you're making, for example, cauliflower cheese and I use ground almonds to thicken curries (adds a great flavour)
Good luck