Panoramas can be a powerful format for presenting landscapes, and for the digital photographer shooting panoramas is actually fairly easy. Best of all it can be done without the aid of any special equipment, and with a little practice and valuable help from your computer, you will be able to produce panoramas as wide as you like.
Some cameras – especially compacts and smartphones – have built in software for aiding in taking panoramas, but even without this you can make beautiful panoramas. Basically you will shoot a series of overlapping photos, and then with the help of software stitch these seamlessly together to form one picture, the panorama.
A Tripod is useful, however should you find yourself without one you will just have to imagine that you are it, and try to maintain a steady position throughout the shoot keeping the camera close to your body. Take one photo at the one end of the intended panorama, and then turn to take another. All the time making sure you keep the camera in an even horizontal plane, and overlapping the previous photo by about 30% (this is needed for the stitching later on). There is no specific maximum number of photos you can use for your panorama, if you want you can make it 360 degrees. However keep in mind that the more photos you input into the panorama-making software, then more processing will have to been done and the the bigger the resulting file will get.
To make the 'seams' invisible it is important the entire series of photos is shot at the same exposure, or at least as close as it is possible. Therefor leaving your camera's settings in 'auto' mode is probably a bad idea. If the scene is not entirely even lit, the camera will adjust the exposure differently for each shoot to achieve a proper exposure. You will need to switch to 'manual' and select the settings best suited for the entire scene, and use these settings on all the shoots. You can use the suggested settings by the camera as a guideline, and accept that some shoots will slightly over- or underexposed according to the camera's readings.
Sometimes you might experience problems with 'ghosting', which is what happens when something in the overlapping parts moves between shots. I often see this with trees moving in the wind. My only advise is to try to avoid placing moving parts in the overlaps.
In addition I have found that it is difficult, to say the least, to obtain a good result using polarizing filters. Since the effect of the filter depends on the angle to the sun, it will create unwanted variations between the shots as you turn. So although this filter is often very useful for landscape photography, I would recommend you do not use it for shooting panoramas.
If your are looking to maximize the resolution of the final image, you might consider shooting with the camera in its upright position.
The last step is to stitch all the photos together, and for this job a number of programs will produce a very good result with little or no further work needed by you. There are several free solutions available such as the Image Composite Editor by Microsoft.