You leave a gap.

1/4" or 3/16" is a good starting place.

You fill the gap with backer rod. Its just a very round, flexible airy foam extrusion that comes in various widths. You can go to a masonry supply store (that sells bricks, treads, flagstone) & they have rolls of the stuff you buy by the foot. For me it was easier to get a 3/4" closed cell Sika 8' backer rod from HD (near concrete colorants) & use a sharp utility knife to cut it into 3/8" quarter rounds. Perfection isn't important. All the backer rod is doing is filling the void AND avoiding a 3-point bond of the caulking (the 3rd point being the bottom of the gap). Stuff the point of the quarterround into the gap & dome the exposed surface. Don't leave too much of a void & don't let the backer rod sit too high up in the gap. Trim excess or pack with more to get say 1/8" of caulk in the center, slightly more at the edges because of the domed backer rod. Remember: backer rod is cheaper than caulk.

If you haven't caulked a tile edge before its probably best to initially put down blue painters tape. Fill with caulk & use a straight edge like a chunk of credit card to do initial shaping. You'll need to pull the tape to do the final shaping. Moisten your finger with water & bind the caulk to the edges so everything is sealed with caulk. Too much water will cause the caulk to become glossy (which will become more matte in time). Too little water will cause more caulk to stick to your finger & preclude a flat joint. If you have a severe tile edge, you want the caulk to be a touch higher to mask that edge.

Be sure to clean the edge of the joint so no caulk remains where it shouldn't be while it's still wet. Don't think it will wear off - it won't.

Use color matched caulk from your grout maker (even if its white) it comes. The hardest part is to estimate how much you need. I have 5 tubes of Mapei caulk remaining.

In an exterior setting you use a polyether sealant & isopropyl alcohol instead of water.

Here is a link that might be useful: Mapei Keracaulk