How do you sharpen a knife?
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.