In general, the workflow goes like this:
- Choose metering area
- Adjust and meter
- Retain the metering
- Compose, focus and shoot
Since there are so many steps, spot metering tends to work better for planned shots, although it can perform quite fast when linked with AF point (details under "Adjusting and metering"). For rapid shooting in changing light, matrix metering would be faster to use, but less precise.
Now, let's see the details for each step.
Choosing metering area
Choose an area for which you have a vision about how it should be exposed. This is the key point of spot metering - executing your vision. At this step, it doesn't matter if the area has to be at the neutral 18% gray level, or something dark/light.
Adjusting and metering
Adjusting means that you set your exposure compensation according to which way from the 18% gray level you want the selected area be exposed. You want it lighter - use a positive compensation; you want it darker - use a negative one. Knowing the zone system will help you determine the amount of exposure you need - adjust exposure by 1 stop for each zone further away from the 5th. In the rare cases you want to go further than offered by exposure compensation range of your camera, you'll have to use manual mode.
Point the camera so that metering spot is lined up with that area. Usually the metering spot is at the center of your viewfinder.
Some cameras allow linking metering to selected AF point; that option is quite sensible for the common case where you focus and set exposure by same object (your subject). It will make your workflow faster as you can combine all three last steps into a single press of shutter - you can perform focusing at the same time and won't waste time recomposing.
Note that in full manual exposure mode, the order of sub-steps is reversed - you first meter, observe where your camera reports the exposure related to neutral level, then adjust any parameter of exposure triangle (or a combination of them) to get desired exposure level for the area.
Retaining the metering
Details of this step depend on your camera model, settings and exposure mode. This step can be skipped if you don't need to recompose for actual shot.
In full manual mode, you don't have to do anything in this step - just stop fiddling with controls and exposure stays as it was set, thank you very much.
In (semi-)automatic modes, however, you have to tell you camera to stay at current exposure level. This can be done activating exposure lock.
On many cameras, holding the shutter button half-pressed can be configured to lock exposure settings, but if it also triggers auto focusing, that would also result in focus locking. In many times that may be okay, but if you're going to significantly recompose and use shallow depth of field, it may cause focus being slightly off. For that reason, you may want to use manual focus or set your camera to use back-button focusing, if it supports that.
The most universal way would be to note exposure parameters, set the camera into manual mode and dial in the same exposure parameters. If there's a chance that the next step will take long time, switching to manual mode should be the preferred way - on most cameras, if not all, exposure lock has a timeout limit in the magnitude of 10 to 30 seconds.
Composing, focusing and shooting
Now that you have the exposure settings in place, you only need to worry about composing the picture, focusing and taking the shot. Details of these operations are already out of scope for this question, as there's nothing specific to spot metering to be done here.