The typical way that women dress for beach volleyball is to wear bikinis. Men typically wear board shorts. However, anything that's comfortable and a little bit loose-fitting is appropriate. It just depends on the temperature.
Beyond clothing, sunglasses are important to protect your eyes from the sun so that you can see the ball better. Many players wear a visor, or some of them wear a hat. If you have long hair it's a good idea to tie it back or braid it to keep it from your face.
Another aspect of beach volleyball is sunscreen. It's important to protect your skin from the sun since you're in it a lot when you're playing. You want to use an SPF of 30 or above. Apply before you go out in the sun, and reapply every couple hours, or if you're in a tournament, after every match.
Also, if the sand's really hot, there are special socks called sand socks that are designed to keep your feet from burning or blistering. If you want to buy sand socks, the common brand is Vincere, and you can buy them online or at local beach shops.
Those are some suggestions on what to wear when you're playing beach volleyball.