There are two discounts for students. The 18+ Student Oyster allows you to purchase travelcards with a 30% discount. This is only really useful if you travel 4 or more days in a week. Single fares and caps are the same as a normal adult Oyster card.
You can also get a 16-25 National Railcard and have the discount added to either a blue adult Oyster or an 18+ Student Oyster. This gives you a third off the adult off-peak single fares and the off-peak cap.