A stone is the hardest way to sharpen a knife. If you don't get the angle exactly right, you'll just be messing up your knife, not sharpening it. If you do want to go that way, yes, you'd definitely want to practice on something cheaper, because it's likely you will mess it up. This is why a lot of people just take their expensive knives to a professional to get sharpened. I've seen good knives sharpened into oblivion before - totally reshaped blades, and still not even really sharp.
Most electric sharpeners are designed to avoid all this - the good ones have a fixed angle sharpening surface, and something to hold the knife in the right orientation, so you can't mess it up. The one caveat is that Western style knives have 20° edges, while Japanese style ones have 15° edges, so for example in the US, the sharpeners you buy won't be good for Japanese style knives.
Additionally, you don't actually need to sharpen them very often at all. Periodically honing your knife will keep it pretty darn sharp, especially if it's a decent knife and you take good care of it otherwise. Give that a try, and you may not feel you need to sharpen it for a long while. At that point, since you won't be sharpening it all that many times in your life, it may not be worth learning to sharpen the hard way - a professional or an electric sharpener will be a lot easier.
But if you do want to get a stone and teach yourself, the thing to do is probably to start with a finer-grained one, so you can't destroy the knife as easily. You can practice getting the angle exactly right, doing finer sharpening. Hopefully that's all you'll need, but if you ever need to do more, once you've got some practice, you can move on to a coarser stone for really reshaping the blade. (Or... you can apparently save money and use sandpaper.)
The user "virtuovice" has some great videos on knife sharpening. It was my introduction to whetstone sharpening and since following his videos, I have been able to sharpen my range of kitchen knives to a pretty incredible sharpness. His videos are mainly aimed at hunting knives, but the techniques can be applied to kitchen knives
Have a look at this video: https://www.youtube.com/watch?v=tc_TEWmMcD0
The main thing to try and remember is to move with your arms and not to rotate your wrists at the ends of each stroke across the stone so that the angle is kept constant. I'd practice on some cheap knives and just go slowly first. Look at how much metal is being removed from the blade - rinse the knife often and check your progress. Imagine you are trying to take a very fine slice of stone off the top surface.
In terms of technique, you can also take a look at this video:
https://www.youtube.com/watch?v=Lm53mCOQTR8
It's easier to see because of the high grind on the blade.
Best Answer
Take a marker to your knife edge so you can actually see how you're removing material from your knife.
Additionally you probably need to get another cheap stone and soak it either in water or oil, depending on what the stone calls for. You want to make sure the stone is producing a paste for you, and you want to make sure your stone is flat. Getting better stones won't really help if you're using the stones incorrectly in the first place. Get a one dollar knife you don't really care about and then sharpen the knife till you develop a burr on one side of the knife. Then Do the same thing on the other side of the knife. Then you want to strop your knife on some news paper or on the edge of some cardboard. The actually motion for stropping a knife is the same as sharpening it only stropping is more forgiving than sharpening is.
Additionally, you want make sure you're stop sharpening your knife at the right grit for what you want it to do. I typically sharpen with sandpaper so I can't really give you grit numbers because natural stones have different grits than sand paper and diamond stones. The general rule of thumb is to start on a lower grit to remove material faster and move to a higher grit to get a more refined edge, then strop to further refined edge and to clean up the blade/remove the burr.
Generally speaking, if you're using a general purpose chef knife, you want to keep a consistent angle of around 20 degrees when you sharpen a knife. The marker you paint the edge with will help show you where you're not doing that. it will also show you where you're removing too much material from the blade and where you're not removing enough material from the blade.
A final thing you want to do is to check your blade for nicks. If your blade has nicks in the edge then you're going to have to remove material till you remove the nick in your blade. That could be the issue you're running into. orient the blades edge towards a source of light above you. If you see any reflection then your knife is not sharp there.
Finally, don't put your knives in the sink, dishwasher, or drawer. These environments are all terrible for your knife edges. You're guaranteed to dull your knives considerably if you do any of these things.
Let me know if something still isn't making sense to you and I'll explain it. I know too much about knives.