It is very hard to describe knife sharpening in text. I'd recommend searching out a few Youtube videos for tips on technique. That said, I'll add my 2 cents worth. Everyone has a different idea of the "correct" way to sharpen a knife; below is just how I was taught.
What is the proper way to sharpen a knife with a stone like this?
If the knife is already sharp and you're touching up, start with one of the fine stones. If not, start with the coarsest. Work your way from coarser to finer. Put some oil on the stone, put the edge of the knife on the stone at the angle you want (try to match the existing angle), then stroke the knife along the stone as if you're trying to remove a fine shaving of stone. Pull the knife as you do it to sharpen the entire edge.
Do I need any other tools?
No. A jig for keeping the sharpening angle can help, but most likely wouldn't be usable with a stone like this.
Do I need any protective equipment?
No, but be very wary of where your fingers are, and where the edge can go if you slip. Keep your fingers out of that area.
Do I have to use some type of oil?
Yes, to carry away the swarf, or metal particles. For cooking knives I use a vegetable oil. Yes, veggie oil can go rancid, but cooking knives are used and washed often enough that it's not an issue.
Is it better to go fast, or slow?
Slow. I like to take long strokes along the whole edge, concentrating on keeping my angle consistent. I use about a 20 degree angle on kitchen knives.
Is the procedure different with a knife that has never been sharpened before?
Only that you would probably start on a coarser stone.
Do I have to do anything different if the blade has rust on it?
Remove the rust first with fine sandpaper.
How do I know when the knife is sharp?
There are many ways to test. The old newspaper test, where you hold a piece of newsprint in one hand and cut it with the other is a good one. You can try shaving your arm hair until you run out :)
But really, watch some videos and just practice.
As far as books, I highly recommend The Complete Book of Woodworking: http://www.amazon.com/The-Complete-Book-Woodworking-Detailed/dp/1890621366/ref=sr_1_1?ie=UTF8&qid=1335885982&sr=8-1. It's easy to follow even for the uninitiated. It goes over the major tools, what they are used for, and has excellent instructions on some starter and intermediate projects. There are even some workbench projects toward the end, one of which is made only from plywood and 2x4 lumber. I made it with a jigsaw and really uneven cuts, and it's held together well for about a year (it's usable for everything except hand planing). I'm also a software engineer by trade and learn well from books, so I spent a good few months obsessing over this book in my apartment before buying a house and really getting started.
For video instruction, The Wood Whisperer is one of my favorites; he gets into what tools are used for, how to set them up and tune them, and has some videos dedicated to safety. He's also very technical and comes from a science background, so the engineer in me relates well with him. He doesn't leave out many details. Fine Woodworking is also very good and for $5 a month you can get access to a ton of video content.
http://www.thewoodwhisperer.com
http://www.finewoodworking.com
SawmillCreek and WoodworkingTalk are nice forums to search through for tips and discussions about what tools are best used for what projects.
http://www.sawmillcreek.org
http://www.woodworkingtalk.com
Most of these will discuss fine woodworking, furniture making, and detailed joinery, which you may or may not be interested in. All of them, however, will give you information you want about tool usage. It may be more detail than what you're interested in for the projects you describe, but if anything you'll be over-prepared.
Best Answer
Be very careful with the grinder. It is only used to establish the original critical angle and to take out nicks in the cutting edge. If you use too heavy a pass and the metal changes color (metal temper color - extremely light straw, you've started to mess up - blue or dull metal color, you've really messed up), you soften the metal and it won't keep an edge till retempered or ground past the area where the coloration occurred.
Once the angle is established, you use standard sharpening stones to keep the edge, they are much finer grit and establish a really sharp edge. On a properly maintained tool with an established angle, this part is a touch-up process, not a laborious grind, and may be done several times during a turning session if maintaining a really sharp edge is necessary.
After fine stone work, you can use a strop charged with buffing compound to remove the burr (wire edge) that results from a good sharpening session. I also just used the buffing wheel on the other grinder (always use the portion of the wheel where the surface is passing away from you so the point doesn't catch and throw the tool at you).