The easiest way: keep track of a yaw variable and pitch variable. When the mouse moves you increase or decrease the yaw or pitch, based on the X and Y movement, respectively.

If you can't directly set the angle the camera is rotated to (or you haven't programmed it yet), reply and I'll show you how to compute the new look at coordinates based on yaw and pitch, or you can use the frustum building functions of the graphics library you are using to help you out. (Can you give some more details, please?)

If, for some reason, you can't keep track of a yaw and pitch variables yourself (and the camera you are using doesn't let you get or set them) then its possible to take the look at coordinates, compute the current angle, change the angle, and then compute new lookat coords.

assuming that X goes to the side, Y goes forward, and Z goes up

float pitchCos = Math.Cos(pitch);
Vector3 offset;
offset.X = Math.Sin(yaw) * pitchCos;
offset.Y = Math.Cos(yaw) * pitchCos;
offset.Z = Math.Sin(pitch);
Vector3 lookat = offset + cameraPos;