With a paring knife or utility knife, cut the top off of the shallot. Make sure to leave the root end intact.
Using the paring knife, make a vertical score down the shallot and peel the papery skin away. Then, break the bulb into separate pieces — there are usually two per shallot.
Sliced
Once you've peeled the shallot, lay it on a flat side. Slice it crosswise into rings. You can cut these as thickly or as thinly as you'd prefer (1/8 or 1/4-inch is usually perfect).
Dice or Mince
Cut the peeled bulbs in half lengthwise, then turn the halves to face flat-side down. Secure the shallot with your non-dominant hand. Make lengthwise cuts (about 1/4 to 1/8-inch thick) up to the root end, but not all the way through.
Make a parallel cut, then rotate the shallot and cut crosswise up to the root end. Once you reach the root, cut it away and discard it, making sure not to waste any shallot.
To mince the shallot, repeat the same process as dicing, but with thinner lengthwise slices and crosswise slices. Once the root end is removed, use a back-and-forth rocker motion with a chef's knife to finely mince the shallots.
Strips
Peel and separate the bulbs the same as before. Then, cut away the root end. Cut it in half lengthwise, then lay each half flat-side down. Make vertical slices as thickly or as thinly as you'd like.