Rongnongno Loc: FL

Gear needed
Support:
If you do not have any, no worries.
If you do the minimal is a tripod and a rail to set the nodal point.
The best is a L bracket that allows vertical movement as the tripod allows for the lateral motion.

Camera:
Any camera can be used.
The camera orientation is not important but must be constant. With a L bracket it is likely the camera will be on portrait position but not necessarily so.

Lens:
When shooting multiple rows this is usually to get more details so use a longer lens than a wide angle. This will have an influence on the overlap as longer lenses do not create as much distortion than a wide angle.

Generality:
When shooting a multiple row it is better to create an odd row number 3, 5, 7.... The center row is the horizontal reference. This is not a rule but best practice.
Depth of field is more important then speed so use your existing knowledge to insure the best acceptable field of focus you can produce.
Removing objects:
Doubling the shots, even tripling. You can remove anything that moved in Post Processing (PP) IF you have spare shots.
Stacking:
Use stacking as you normally do per frame before stitching.
HDR:
HDR presents some difficulties. If you do it prior to stitching chances are that you will run into trouble. HDR is still possible this way if your PP software allows for synchronization of the frames. Still I would do that after stitching.

Shooting methods:
Handheld: Disregard the row instructions above and even disregard the recommended overlap. Shoot as many frames as you dare. Just make sure the camera orientation stays the same and that you cover the panorama area you want you want create plus a few frames outside.

Specialized gear: Read the manual that came with it.

Tripod:
Preparation:
You need to be organized and logical.
Level the tripod head. Level the panoramic head too.
Shoot by rows or by columns. Do not mix for convenience's sake, even if some software will correct this.
Shoot with the same camera orientation.

Determining capture points:
The only tricky part is to set the capture points so that you create all the overlaps needed to stitch in a consistent manner.
Using the camera set horizontally, orient it toward the left so that the limit of the panorama in in the right side of the camera viewer. Set a '0' mark here. You do not need to bother with the right side yet. (You can do that from the right side too)
Tilt the camera upward. When the camera view overlaps the previous view as intended (1/3 for a 80mm lens, less if the lens is longer). Set a '1' mark there.
Still moving upward, keep marking the vertical scale until the camera viewer is above your intended panorama upper limit.
Return the camera to position '0'.
Tilt the camera downward. Process is the same as above.
Every mark created correspond to a row.
Set the camera back to the zero mark.
Mark the horizontal support.
Rotate the camera to the right until the camera viewer has the appropriate overlap. Mark it.
Keep going until the camera viewer is out of the panorama, at the last mark.
Every mark correspond to a column.

Shooting
Best procedure is to start from the top row (left to right or right to left, your choice).
The reason is that the sky can change color during the shoot so taking this out of the way is a big deal.
Tilt the camera up to the desired FIRST marked position. Take the capture.
Rotate the camera (as per your choice of direction) and stop at the next mark. Take the capture.
Do this until you are on the other side of the panorama.
Tilt the camera down.
Start the camera rotation again.
Here you have the choice of returning to the first horizontal capture mark or just swivel the camera in the other direction, taking a shot at each mark.
Repeat until you have shot once* at every mark and the camera is at the exact opposite from the point you stated at. (Low right or low left depending on your choice)

Use manual focusing.
White Balance, exposure settings must be set to manual so that they stay fixed for the entire series.
Shooting raw files helps in wide dynamic range situations.
Work fast, light changes faster than you think.
If you can, use hyper-focal distance to give you good depth of field.

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* Or more for stacking** or removing unwanted 'guests'.
** The only case where you will 'play' with the focusing.

This is written in collaboration with Gene and RGG.

Gene51 Loc: Yonkers, NY, now in LSD (LowerSlowerDelaware)

I would add that white balance should not be set to auto, and exposure settings should remain fixed for the entire series. Shooting raw files helps in wide dynamic range situations and better quality adjustments in post processing. HDR is always an option. Determine your exposure for the entire scene based on the worst case scenario. When the scene includes clouds, use the camera's spotmeter or a hand held spotmeter to measure the clouds, and set your camera 1 to 1-2/3 stops brighter than the meter reading - this will ensure that you do not blow out the clouds and you retain the ability to recover the highlights in post processing. Use that reading for the entire scene - consistency of exposure is key to seamless stitching. Work fast, as things will change faster than you think. If you can use hyperfocal distance to give you good depth of field without resorting to making multiple exposures at different focus points for focus stacking for each part of the image, it will make things a bit faster and more predictable. The last thing you want to see is a 3 row 15 shot pano with one or more of the images not quite right. If you need to focus stack or HDR and you are shooting a natural subject with things that move, like trees in the wind, try and plan for a calm day.

But the most important thing is to remember to smile and have a great time!