In this section of the tutorial I will be using Adobe Photoshop Elements 5 to stitch the shots together into a panorama, however most popular photo-editing programs have a similar feature that works in much the same way. It's normally a fully automated process, so just refer to your program's instruction manual or help files.
When you download the photos from your camera, it's a good idea to put the ones that you want to turn into a panorama into a separate folder; it makes them a lot easier to find later.
Start up your editing program, and find the automated photo-stitching tool. In Adobe Photoshop Elements it is called Photomerge, and is found in the File menu under "New". If you click on this you'll see a simple dialogue window with an option to browse to the location of the folder containing your panorama shots. Go there, highlight all the shots you want to include in your merged panorama and click OK. Note that if you have the shots already open in your editor then they will be selected automatically, but since having photos open in the editing program uses up memory, the merging process will go faster if you leave them closed and use the dialogue browser instead.
Once you click OK the merging process starts, and it is completely automatic. It will take a while to complete, possibly quite a long while if you have a slow computer and/or very large image files. However sooner or later it will finish, and you'll see a preview of the finished result that looks something like the screen below. If there's a lot of sky in your shot, as there is here, checking the Advanced Blending button will help even out any slight exposure variations. Simply click OK to conform and finish the process.
And before you say anything, yes I violated my own first rule, and I didn't use a tripod for these shots, because I'm an idiot and I'd left it in the car. But at least I remembered to use a focal length of 50mm and manual exposure, so I should be able to do something with it. Fortunately for really stupid people like me Photoshop Elements has a handy tool to straighten tilted horizons. After flattening the image to a single layer, simply click on the tool and drag a line along the horizon to straighten the whole image.
All that remains is to crop the image to chop off any uneven edges. Of course if you remembered to use a tripod there wouldn't be as much to crop off at the top and bottom, but with a shot like this it's the horizontal coverage that's important. If anyone's at all curious, the town in the shot is the beautiful French port of Collioure, on the south coast very near the Spanish border.