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Grout is one of those things that you don't notice if everything is ok, but that you see when something is wrong. It is similar to mortar (indeed, some types are almost identical) but I'll be tackling mortar in a followup article as I think its history and uses warrant a deeper look.

For our purposes grout will be considered as material that is used to close gaps between tiles or stone, limited to 1.5 inches (3cm) in width.

Tools and accessories for tiling and grout

A mixer attachment for your drill. Seriously, don't mix by hand. It's exhausting and your grout will still be unevenly mixed.
A high-quality tiling float for forcing grout evenly into the cracks
Bulky sponges that can help you wipe away excess material
A good grout saw if you are removing old grout
A couple of buckets for cleaning up the excess

You'll of course need grout and you'll need some sort of sealer if you go with a cement-based grout, but that's getting ahead of ourselves.

Step 1: Types of Grout

There are a few types of grout which we should talk about. They fall into two main families: cement-based and epoxy-based.

Cement-based grout

Cement-based grount uses common Portland cement as the binding agent. You have two main variants of cement-based grouts: sanded and unsanded grout. The difference is whether or not you have sand in the grout or not. When mixing concrete (for a slab, sidewalk, etc.) you use about 1/3 sand as a filler to bulk up the mass of the concrete and reduce the cost of the area you are trying to fill. So for tiling it is very much the same. The wider the space in your tiling, the more likely you are to need to add sand to your mixture.

I have a rule of thumbs for sand in grout: if it is wider than your two thumbs, add sand!

Because cement is a relatively cheap material, the cost of this type of grout is cheaper ($2-4 per pound) than epoxy-based grout.

Cement-based grout can't generally be stored for more than a year. Once you've bought it, and definitely once you've opened it, you'll need to use it as soon as you can. If it is more than a year old, toss it and buy some more.

Epoxy-base grout

The other type of grout is epoxy-based grout. As with all epoxies it comes in two part that you need to mix together thoroughly. It is harder to work with. It can set up on you part way through a large project (which can be a huge headache) and it can be a chore to clean up. The pluses are that it handles wear really well, and won't crack with age. If you are installing tiles in a high-traffic area, either on the floor or in a public place, epoxy-based grout is probably a good option for you.

Epoxy-based grout is more expensive ($8+ per pound) than cement-based grout.

An added bonus is that properly stored it will last a very long time. Once you buy it, if you don't use it all, you'll have quick access to it in the future.

Step 2: About Coloring Grout and Using Pigments

One of the neat things about grout is that you can color it using pigments to match your design and style. These pigments come in a large selection and you have many, many options to choose from. As you can see it's really kind of endless.

A couple of things to keep in mind when selecting grout:

Grout darkens with time - you should aim for a few shades lighter than what you will actually see initially.
Test your colors before you commit - set up a small panel with some extra tiles, and fill it with a couple of color options and let it set for a day or two. You'll be able to really get a feel for the match this way, and you will be less likely to end up selecting a color you'll hate.

Step 3: Sealing Your Grout

Cement-based grout is porous and stains easily. You'll have to seal it properly if you want to avoid unsightly darkening. This is especially true in a kitchen, but also around sinks, toilets, and tubs in bathrooms. We sealed all the grout in the tiled floors in our house because we want it to last.

If you have dingy, dirty stains in your grout you can hire a professional cleaner to steam your tiles and scrub out the mess. If you're of a mind to do it yourself, all it really takes is a good degreasing agent and a set of stiff bristle brushes for cleaning tiles. Oh, and a lot of elbow grease!

I will add that I got one of these spinner cleaner things and while it did a good job, I can't say that I'm a huge fan.

Once you've got everything clean, you should look into one of these sealers:

Tuff Duck Granite, Grout and Marble Sealer 1 Quart Stone Tile
Serveon Sealants H2Seal H2100 Stone Sealer - Professional Grade for Natural Stone, Grout, Brick, Tile and Artificial Stone (1 Gallon, Stone Sealer)
Miracle Sealants PLUS QT SG 511 Porous Plus Penetrating Sealer, Quart, 2 Pack

A good sealer applicator will also make you life much easier.

Step 4: Applying Grout to Tiles

Most of the real work when applying grout to tiles comes before you even start. It is all in the setup and how well you've tiled your work area.

The means that your tiles have even spacing and level surfaces.

If you are reapplying grout to old tiles, you can clear out the old grout with a grout saw, or a grout removal bit for a dremel.

If these are new tiles you have to wait for the mortar you've used to attach the tiles to dry! Don't apply grout if the mortar isn't 100% dry!

Once you're ready to start, the process for applying grout to tiles is very straightforward.

Select your grout color - do a test against your tiles. You're living on the wild side if you don't. The grout is wet and will dry a different color than what you see in front of you. As I said before, it will darken with time, so take this into account. Choose a dark color for high traffic areas. White or light-colored grout will be difficult to keep clean!
Mix your grout according to the instructions - I like to do 2/3 of the water and then add the last 1/3 slowly, working my way up to the exact consistency that I need. You are aiming for a cake batter consistency. Don't make it too watery! It should be thick and even.
If you are doing a floor, start at the farthest corner from the entrance to the room - you don't want to get trapped in a corner :)
Plop your grout directly over the tiles - use your float to push it down into the cracks.
Clean up the excess - After you've applied your grout, wait 15 minutes or so and go get two buckets of water and your sponge. Use one bucket as your clean water, and the other to clean you sponge in. Wipe your floor clean and try not to over-saturate your grout with water. You want the grout to sit just below the surface of your tiles, so don't push down too hard.

Literally, rinse and repeat :) Keep going, you can do it!

If you've done your own grout, post some pictures below. I'd love to see!