When you approach the net to hit a tennis volley, you need to switch your grip to an appropriate volleying grip. A continental grip, or something close to it, is acceptable. For a more in-depth description of how to find a continental grip, you can check out the grips section of the website. To briefly review, the heel pad and index knuckle need to rest on the second bevel of the tennis racket handle.
The reason you want to hit with a continental grip, or something close to it, is because it allows you to get the strings facing the correct direction (at the tennis ball) on either the forehand or backhand side. At about 45 seconds into the video, I demonstrate how this works. Because you are at net, you don’t have enough time to switch your grip. Most of the time, you are quickly reacting to where your opponent has hit the ball.