You can also purchase a towel pack from Housekeeping (call them and ask for a towel pack) that includes four bath towels, two hand towels, four face cloths and a tub mat for $6. They will pick up the extra towels on day four and you'll need to purchase another towel pack if you need more towels.
Otherwise, bring some from home. Do not grab towels from the pool to use in your villa. They cost more to launder and DVC members have been asked not to use the pool towels in the villas, but use the acceptable alternatives.
One more thing, if you are only there seven nights or less, your room will not be cleaned. The trash will be picked up daily (the dreaded daily room check) and on day four your towels and supplies will be replaced. Your beds will not be made and sheets will not be changed. The room will not be vacuumed, but you will have a vacuum in the room to vacuum the room if you want. Otherwise, all the coffee you get is what is in the room on day one and again on day 4. Usually it is one or two coffee filter packs (makes roughly 4-6 cups). If you drink more coffee, bring your own coffee filters (flat bottom basket style - Mr Coffee type) and coffee. You might have shampoo, conditioner, shower gel dispensers mounted on the shower wall. Or you might get the small 2 oz bottles of shampoo conditioner and shower gel. If you need more, bring it from home. If you are there eight nights or more, you will get a full cleaning on day 4 that makes the beds, vacuums, washes any dirty dishes, replaces supplies.
If you need anything not in the room, plan on buying more. DVC is a timeshare and owners pay for everything. Since you are purchasing a reservation from an owner, your stay will be the same as theirs.