Go do a practice shop. Ask all the questions you need to there. Make up a story like, "I was thinking of giving someone a lottery ticket for her birthday but I've never bought one before." When you do the real shop you'll be more relaxed. You don't even need to actually buy one in the practice shop, just say, "Her birthday is coming up in two weeks so I'll get one just before that day if I decide to do this." (Have a date picked out just in case they ask, "Oh really, what day? My wife's birthday is coming up too."
Be sure to find out the prices of the tickets. Some of the multi-state lotteries are $2. The local lottery may be only $1. Or maybe they're all $2 these days. But know which one you will get and what it will cost. Find out if you have to pick your own numbers or do a "quick pick" where the machine randomly picks the numbers for you. If you're required to fill out your own ticket, ask the clerk on the test shop how you fill it out. I've never done a shop where I could get a lottery ticket so I don't know the requirements. But there are several games to choose from generally, I know that much.
I only get tickets when it's in the mega millions, and half the time I don't remember in time even then.
Time to build a bigger bridge.