The most common way to do this is to put your camera on a tripod, take one picture, turn the camera for a specified angle take the next picture and so on, until you are done. In practice you should have an overlap of about one third of your image (20 to 30%) width for each image pair. You do not need a digital camera, but in the long run this is cheaper.
Many lenses produce barrel- or pincushion distortion and these errors would have to be corrected before trying to join your pictures.
The next step is to put your images together, so that one single picture is created, which shows the whole panorama. This is called stitching. In practice the single images have to be warped into a common perspective, because a regular camera projects objects on a plane but a panoramic picture projects objects on a cylinder or a sphere. The parameters of the warping depend on your lens and how your camera was oriented while shooting the pictures.
Very often brightness in the overlapping areas do not match exactly so that the individual images have to be crossfaded into each other.
A common way to view panoramic images is to use special viewers e.g. QuickTimeVR or Live Picture's Zoomit. So your image has to be converted to the corresponding viewer format.