1. Don't ask, "Did you kill anyone?"
Don't bring back bad memories.
2. Offer to pay for their check.
If you see a Veteran wearing a unit hat at a restaurant, you can offer to pay for their check. Even if they don't accept your payment, they'll feel honored.
3. Ask them about their service, but see #1.
Ask them about their unit or what they did for the military. It'll likely bring back good memories. Just don't ask about killing people.
4. Offer to buy them a drink, and see #3.
Offer to buy them a drink. Ask about their service. Just don't go to excess with buying them drinks. There are a lot of service members with alcohol or former alcohol-based problems.
5. Find out about the military.
Find out about the service. This will give some common ground to understand when you ask about their service. I have had people ask if the infantry took care of babies. Ugh.
6. Buy them a gift card.
A gift card, even of small denominations, will be a great way to show your appreciation and make sure the business you support is paid for their service, rather than spent on rent (or whatever).