Regular resort guests and
DVC members using DVC discount can reserve tee times up to 90 days in advance. Based on experience, you can usually get what you want calling 30 days in advance if trying to get a weekend or holiday and 14 days in advance for other days of the week. You can make tee times via phone or on-line.
For DVC, You can purchase an annual DVC golf card for $50 plus tax and then use it to get a discount per round for member and up to 3 persons playing with the member. You buy card at pro shop and don't need it to make tee times; you just purchase when you go to first tee time.
Whether you should buy the card is a different question. It gives you 25% off the resort guest price for before 10 am times and 40% for after ten times. Since the card costs $50, you need to accumulate enough discounts to justify buying the card and thus if you are only going to play once or twice during a year, you likely should not do so.
Also, though the 40% discount for after 10 times is one of the best discounts, that 25% pre-10 discount is not, particularly if you will play an even number of rounds. Disney offers a 2-round pass to any resort guests that gives you two rounds at a discounted price and that price per round is often less than or very close to the DVC discount per round for pre-ten, making the 2-day pass the better deal for pre-ten times if you play an even nnumber of rounds because you don't have to pay $50 for the annual golf card.