Mead is back sweetened to add sweetness after fermentation is complete. In order to back sweeten mead, it must first be stabilized. Attempting to back sweeten a non-stable mead will not work in most cases.
Mead that is too dry can be unbalanced. A dry mead may be too acidic, or a spicy mead too one-dimensional.
Flavorings that rely upon sweetness for context (like honey and fruit) can be delicate or even indistinct. Even a melomel with a large fruit load may be unrecognizable in the absence of sugar. Adjusting the sweetness level can bring these flavors back into focus.
Back sweetening is best done after the mead is mostly clear. Yeast and particulate matter significantly change the flavor of a mead and can throw the balance far off. It's also best to do immediately after racking off the lees, because you'll be stirring the must. There's no reason to re-suspend particulate matter that has already dropped out.
If you don't know your desired sweetness level (a specific gravity reading), take a large sample from the fermenter. Sweeten it in stages (use your hydrometer to measure how sweet) and draw a small sample into a tasting glass each time. For example, you may end up with samples at 1.000 (unchanged), 1.010, 1.020, and 1.030. It can be helpful to remember that you can blend sweetened samples to reach a desired gravity reading. A 1:1 blend of 1.000 and 1.030 samples will yield a sample with a gravity reading of 1.015.
Taste each sample and determine the level of sweetness you desire. If you've narrowed it down but can't decide, it can be helpful to clear your palate with crackers and water, or ask for a second opinion from a friend.
Once you know your desired final gravity, calculate how much additional honey is required to raise the current specific gravity using the following formula:
[Desired Gravity Increase] / .035 * [batch size in gallons] = X pounds of honey
For example, the current specific gravity of a 5 gallon batch is 1.000 and the desired specific gravity is 1.025.
[.025] / .035 * 5 = 3.6 pounds of honey
Not all honey contains exactly the same amount of moisture or sugar, so it's safe to start with one half or three quarters of the calculated amount and adjust upwards. In this example, you could add half of 3.6 pounds of honey (1.8 pounds of honey), discover that the gravity is 1.015 (higher than the expected 1.012-1.013) and then carefully step it up to your desired final gravity without over shooting. It's easy to add more sugar. It's hard to take it out.
When mixing honey into mead, you will need to stir it gently. Vigorous stirring, creating a whirlpool and agitating the surface can cause excessive oxygen contact. It may take a while to dissolve the honey, but patience will pay off. This is easiest to do with a drill and mix-stir set to a low speed.
You can speed the process along by warming the honey in a hot tap water bath beforehand. Just be sure to dry the container so that unsanitized water doesn't drip into the mead. You can also choose to more vigorously mix a smaller portion of the mead with the honey in a separate container, then add it all back to the fermenter.
To reiterate: patience is best. If some small globules of honey in the corners aren't dissolving after a few minutes, leave them be. They'll dissolve on their own in a few days.
After you hit your desired final gravity, give it time to clear up, do any final processing like fining or filtration, and confirm that fermentation has not restarted by checking that the specific gravity has not fallen below your desired final gravity.
An alternative to back sweetening with honey or another fermentable sugar is to use a nonfermentable sugar like lactose or xylitol. This has the advantage that you don't have to worry about renewed fermentation. Some artificial sweeteners have short shelf lives. (If you've ever wondered why diet soda expires so quickly, this is why!) Others have distinct tastes or aren't terribly sweet-tasting to start with. Before using these in a large batch, you may wish to experiment on a smaller scale.