As I am a college student, I somewhat by default live in a college town. Being a college town, many of the local stores offer student discounts. Not all of them will tell you about having a student discount however. Which, frankly, I find strange because it seems to me that part of the point of having a student discount is to encourage students to come spend money at your establishment.
Basically there are three types of stores.
1. Sees that you are of college age, and either asks if you are a student and want to discount, or just assumes and gives you the discount. This personally is my favorite type. The store makes it clear that they want your business and does what they can to encourage that. I went out to dinner with a friend a little while ago and when we got the check, the waiter told us he'd already applied the student discount. This level of service is awesome. I will definitely be going back, both because of this and because the food was really good.
2. Has a sign or is very public about the discount, but generally waits for you to prompt them about getting the discount. Honestly, this is fine. I respect that they don't want to lose money giving the discount to people who look college age but aren't, and they've made it clear that it's there for the asking. The best places will take you at your word if you ask for the discount, though some will usually ask to see ID, though if you're in a large group of students, they may just take your word for it. The point is they have this discount to try and get customers, and they know it. The best example of this is the local movie theater.
Then there's the last type.
3. Has a discount, but won't mention it, and sometimes even get annoyed if you ask, because people behind you in line hear you asking and know to ask. Why have a discount if you don't want to offer it? I mean really. If you don't want to do it, no one is forcing you. The main place I've run into this is a local ice cream store. To be fair, they don't need a student discount to draw in students. I think it's nice that they have it, but honestly, I'd rather they stop offering it than have them getting annoyed whenever I pull out my ID and ask for the student discount.