Like most natural stone tiles, slate is somewhat porous, which can mean trouble in terms of absorbing stains and moisture. This may not be much of an issue for a slate wall in your study or den, but in most places you'd use slate---the kitchen, the bathroom, or any floor---you'll want the added protection of a tile sealer. If your slate doesn't come pre-sealed, do it yourself during and after the installation process. Water-based sealer is generally preferred over oil-based because it won't yellow over time.
Choosing a Sealer
Sealer can give tiles that shiny, glazed look you often see---but it doesn't have to. Matt finishes are a softer, less shiny option, and still provide the same level of protection. Which you choose should depend partly on your tastes, and partly on the way the tile is being used. Wall tiles for kitchens should generally be at least semigloss to allow for easy cleanup of grease and food. Floor tiles anywhere should be matt to prevent slipping. Bathroom wall tiles, especially in the shower, should usually be high-gloss, so mildew can't take hold as easily.
Unsealed slate will absorb stains from just about any source---including the grout used between the lines of the tiles during installation. This presents a complicated problem, because grout is applied by wiping it over the face of the tile, pressing it into the lines, letting it sit for a minute, then wiping down the tile with a damp sponge. Before you grout, use a paint brush to apply a coat of tile sealer to the face of the tiles, but not the sides inside the lines. That way, the grout will stick inside the lines, but it won't stick to the tile face.
After you've grouted the slate, it needs to be sealed again, grout and all, but not right away. Grout takes a few days to completely dry and set, and if there's any moisture left in the grout when you seal, the seal will be compromised. To be safe, wait a day for the grout to set, then thoroughly clean the whole surface, then wait another three or four days for it to dry out. Then apply the sealant over the whole surface as instructed. It should be resealed every year or two.