Right, here's a quick guide to grouting using a washboy. It's a modified version of a previous post I made. It's looong.
A guide to grouting using a washboy and a spongefloat
Grouting basics
Only grout and clean one surface at a time, and if it is large, you may want to divide it into sections. Doing this ensures the grout doesn't dry up too much. Bear in mind that you don't want the grout to be too fresh/wet either. If it is too wet, the additional water on the sponge will weaken the grout. You have to find a compromise between ease of cleaning, and the amount of time you wait before cleaning, up to a certain point. Wait to long after application and the job will be botched. Wait to little, and the grout will crumble after a few months.
Do consider, that though the manufacturers usually recommend you leave the grout to set for ten to fifteen minutes, it really depends on the nature of the tiles. If they're very porous, they absorb alot of the water from the grout very quickly. If they're very dense and absorb very little moisture, you need to leave it to set for a bit longer, which allows you to grout larger sections at a time. You'll get a feel for it after a few times.
Mixing
ALWAYS, and I cannot stress this enough, use clean tools. Old adhesive or grout residue will accelerate the curing of the grout, and that'll compromise the quality of the end result. Any dirt might cause discolouration of the grout as well.
If you don't measure the amount of water and powder you use, you generally want the grout to be about the consistency of mayonaise. This depends on the type and brand of grout you use. It's easier to measure if you've got a graded scoop and bucket or similar, and it's also recommended you do.
Know this: mixing by hand is pretty useless unless it's a really small batch. Those who say you can't get a proper result using an electrical mixer, probably used a regular high-RPM drill and some cheap paddle, instead of a proper low-RPM mortar mixer and a proper grout paddle.
In fact, you're more likely to get a bad result when you mix by hand, than you are when using a proper mixer. The grout is supposed to be completely homogenous, and there can't be any lumps. By using a proper grout paddle and a low-RPM mortar mixer, you'll avoid mixing air into it.
Before you start grouting, let the grout "rest" for about two minutes in the bucket, and then mix it once more. This produces a perfect consistency if you've done everything else right.
Grouting
Pick some grout up with a bucket trowel or similar, and put it onto your grout float.
If you're grouting a wall, always begin from the top. This is because you want to start from the top when washing too, or you'll have to go over the entire thing again just to clean away drippage. Also, where you started grouting, will have had the longest time to set when you start washing, so it's only logical to start there.
Put the grout onto the wall, begining high, with a vertical motion. Don't press hard.
Start going over the grout with firm 45 degree motions. This works the grout into the grout lines, and avoids "digging" grout out.
You want there to be as little grout as possible left on the tiles themselves when you start washing off.
If you're grouting a floor, put the grout directly onto it from the bucket or the trowel. "Push" it infront of the grout float using an "S"-like motion.
I tend to begin in the corners, both on walls and floors. Make sure to not grout the corner grout lines if you intend to Silicon them.
Washboy basics
Fill the washboy with cold, clean water, so that it covers the grating by around 2-3 cm.
Wet/clean the sponge. If the float is dirty, you'll remove the "muck" by pressing against the grating.
Remove the excess water. Do this by going over the rollers with the sponge float once, then stopping with one end "flat" against the rollers, and then "squeese" the end dry by tilting the float up to an angle of about 45 degrees. Repeat on the other end, and go over the rollers with the entire float again. If the sponge leaks water when going over the roller the last time, you need to repeat. You want the sponge float to be as clean as possible, and damp, not wet. Too much water can damage the grouting mortar, making it brittle and unevenly coloured.
Washing
Go over the tiles in a circular motion with the sponge float. Your objective in this stage isn't cleaning, but to even out the grout.
The circular motion also cleans away the worst excess, but leaves enough to work with when cleaning. Clean the sponge as needed, but not too often. Fill out any gaps in the grouting as needed. Often, you just need to use a finger.
When the grout is fairly even, you can start removing the excess grout. Do this by pressing the float firmly against the surface, and going slooowly in a horisontal motion. Start from the top. Clean just as you start noting the float leaving as "track".
Any dirty excess water drips downwards, and by keeping the motion horisontal, you clean the drip up as you go.
If there is a "film" on the tiles, wait a few minutes for the grout to become a little bit dryer to the touch, and go over the surface lightly with the float. Make sure it is just damp with clean water. To much water may weaken the grout; dirty water is counterproductive. After a few hours, you can go over the grouted surfaces with a clean piece of cloth in order to clean away any residue on the tiles.
Cleaning grout is about finding a good compromise between speed and the quality of the result, which works for you and your way of working. Some techniques require loads of time, but produce perfect results, and vice versa.
As you get more experienced, you'll need less time to produce a good result.
Final notes
I find that my technique is sufficiently fast for the most part, and the result is as close to perfect I can get within a reasonable amount of time.
When you're done grouting, empty the water somewhere you don't risk causing a blockage. In the bottom of the washboy, there will be a layer of cement. If it's new, it'll be lose, and you can scrape it out, or wash it out with a hose. If it's been there for a day or so, or if you've been doing lots of grouting, then you can "tap" it out, by putting the washboy upside down, and tapping with the handle of a trowel round the edges. Do not tap in the middle, as you might crack the plastic if you tap too hard.