Nuts are very well-labeled (by law) on packaged foods, and some people are so sensitive to the presence of nut proteins that products made in facilities that also process nuts are clearly labeled, too. (I’ve only had two clients for whom this was an issue, but be sure to err on the side of caution.)
The main concern for people with severe nut allergies (like my son Adam) is unpackaged foods – like cookies in the bakery section at the grocery store, or bake sale goods. Dining out is also an issue: be sure to ask (and ask again!) about nut oils in salad dressings, and nuts in all other foods (in one now-famous case, peanut butter was used as a thickener in chili).
Cross-contamination is another issue – one that’s true for all food allergens, but tends to be the most severe for nut allergies, in which even a minute amount of nut protein can trigger a reaction. So when dining out, find places that are aware of and sensitive to this issue, and don’t ever be afraid to ask. (It also bears repeating here, always carry your EpiPen, and make sure that the people you’re with know what it is and how to use it!)