SHALLOT
Shallot is an onion, essentially the same species Allium cepa, but it is a variation (scientifically called ascalonicum) that originated as a regular onion in Asia but somehow during the spread of it around the world several varieties arose. Shallot is one of them. There are many things in common when it comes to the onion (Allium) family that also encompasses garlic, leeks, scallions, red onions etc. One good thing to know about onions in general is that they don't accumulate starch, as many other vegetables, but rather collect fructose. If these fructose molecules are exposed to long cooking then they will break down into sweet sugars, which you may have noticed if you e.g. roasted a garlic or a shallot in your oven. This simple trick is widely utilized in kitchens, and it is also of importance to use this slow cooking technique for all onions, including garlic, to give them the sweet taste you are looking for.
Another thing that happens inside the shallot when it is cooked is its slow decay of the strong pungency that it carries when it's raw. This pungency is normally a defense mechanism against predators, but if we cook it we can change it into a nicely tasting tongue-enticing flavor. Of course, shallots can also be used raw in moderate amounts if we need to give some sting to a dish. Conclusively then: shallots will taste differently depending on how you cook them, and if you cook them. Slow cooking gives sweetness and less pungency, while raw shallots are more pungent than sweet.
To mention other cooking techniques - blanching the shallots will give them a mild aroma, also when they are cooked in butter. For some reason, cooking shallots in oils gives them more flavor that hits the tongue and palate.
The pungency of the shallot, and other onions, which is also the pungency that makes us cry when we chop them, comes from breaking down the onion tissue (i.e. by chopping or chewing). As we do so, a special enzyme becomes released from the onion cells and starts to quickly convert non-pungent molecules into highly volatile attackers that hit our eyes or palates. This is why we cry when we chop onions - these attackers have a very good affinity for our eyes that are highly innervated. What can we do about it? An old trick is to simply chill the shallot or onion before we start to chop it. Low temperature minimizes the activity of this ammo-generating enzyme. Another trick is to wear goggles. Some people suggesting having a candlelight burning around your onion, but this never worked out for me personally (the idea is that the flame would burn the volatile pungent molecules before they reach our eyes, but this requires a wide fire distribution to make it work - not very effective with a candlelight). So, unless you are a pyroman, you better stay away from the fire and use a refrigerator as an anti-crying aid.
To see how to chop shallot, at least this is one way to do so, go here.
On with the cooking then. Once you chop the shallots and want to serve them raw, you can always rinse them in water to reduce the amount of pungency. Just throw them into cold water for a while, and change the water from time to time. That will keep them crunchy and useful. You can also blanch them briefly in boiling water, or briefly sauté in a pan, so they taste milder.
Shallots have their seasonal peak in the fall, and they can be used for lots of purposes - either pungency of the raw onion flavor, or the sweetness of cooked shallots. They work well with mushrooms, apples, tomatoes, sauces, cream, or bacon - just to name a few good combinations.
When buying shallots look for the ones that feel firm and not soft, are unblemished, without any strange spots or molded sectors.