Three grains contain gluten: wheat, barley, and rye. You’ll do well with rice, corn, millet, quinoa, amaranth, and buckwheat, since they are naturally gluten-free. Also, there is no gluten in vegetables, fruits, beans, soy products, etc.
But here is the tricky part. If you have celiac disease, even the slightest trace of gluten can cause a reaction, so you’ll need to read labels. For example, soy sauce contains wheat, while tamari does not. Gluten sneaks into beer and countless other foods.
To make life easier, it pays to emphasize simple, mostly unprocessed foods. After all, an orange, an apple, or a serving of rice or carrots has no long list of ingredients that you need to plow through. These simple “one-ingredient” foods are obviously gluten-free and safe for you to enjoy.
Restaurant dining can be challenging, because it’s hard to know what is in their foods. But Indian, Mexican, and Middle Eastern fare will be easiest. Often, celiac or gluten-free support groups in your area will know the best restaurants.
Oats do not normally contain gluten. However, some grains, including oats, can pick up bits of gluten in the field or factory. So some companies (e.g., Bob's Red Mill) have set up dedicated production facilities that prevent cross-contamination.