Onion test: Does the knife "fall" through the onion without effort? The fall test will tell you if the knife is sharp or not. Onion tests are great because chopping them is common to so many dishes. Other onion tests which indicate dullness to extreme dullness are crying and color. Does the onion cause crying (sign that the knife is crushing through cell walls, rather than separating them)? Does the onion discolors where the knife touched it? How long did it take to show? Discoloration is caused by the same thing, and indicates a knife which should be sharpened immediately. "Crying" is more sensitive with stainless knives; with carbon they appear at about the same time.
Carrot Test: Similar to the fall through test. Does the knife cut the carrot or split it?
Pepper Test (Completing the Trinity): Will the knife push cut through the skin of a tough pepper effortlessly, or is some "slice" action required
Mushroom Test: Will the knife slice through or chop a mushroom that's been a few days in the refrigerator without any crumbling.
For me and people who cut like me, these test are compromised a bit because our chopping action is a combination of push, shear and slice. I.e., the dreaded "knife skills" way. In fact, part of its raison d'etre is to compensate for a knife which might be a little dull. This means some cutting tests aren't as revealing as they might otherwise be and leads to the tomato tests described by Chris. Also the Mechanical, Finger, and Forum tests.
Steel Test: After a (correctly done) steeling, was the edge fully restored to "very sharp?"
Steeling or "Touching Up" Just Because Test: Scheduling things before they're needed isn't a test really a test, but it's good practice. I used to steel before I needed it as a prophylactic, but the last year have been steeling only when I feel the need to save the knives some wear. If you choose not to use a steel, you should be "touching" up your UX-10 on your 4K stone something like every couple of hours of knife prep time to freshen the metal at the edge and bevels, and to correct any minor out-of-true issues caused by board impact. Again, a knife that won't steel to better than adequate is a knife that's ready for the stones. Adequate isn't.
Bic Test: This tests polish more than keeness, but it's an excellent test and good for people who like metrics. Slide the knife down the smooth face of a plastic pen as though you were steeling the edge. You'll feel any imperfections in the edge -- whether roll, wave or micro-chip. While you won't feel wear per se, knives never wear evenly and you will feel the unevenness.
Sharpness Tester Test: Just like the Bic Test but with an official, approved piece of equipment that costs money (but not much). You can buy one from Jim Juranitch. He's got an e-tail site which I think is called The Razor Edge or The Razor's Edge or something like that. He wrote (and sells) the best book ever on sharpening for those who use oilstones.
Paper Tests: Hold a piece of paper by the corner out in front of you. Try and slice through the edge with your knife at about a 30* angle of knife to paper's edge. In theory, a sharp knife will cut paper, a dull knife won't. In practice, performance has a lot to do with what kind of paper, how you old it, how you move the knife, and which part of the edge you use (heel's more effective than tip). Once you get the hang of it, you can trust your own testing. But don't read too much into other peoples'.
Thumb Drag: Everybody does this one. For some reason, when they get into fancy schmancy knives they stop trusting it. Let your faith be restored. It not only works, it's excellent -- as long as you don't stop with testing one spot. Drag your thumb up and over the edge without too much pressure. Repeat several times along the edge, and from both sides. A barely sharp knife will feel, well, barely sharp knife. A sharp knife will feel scratchy. Sharper feels itchy. Very sharp feels tingly. Super sharp feels "electric," you may not just feel it on your thumb, but possibly on the back of your neck as well. Calibrate your senses for it by (carefully) thumb dragging a fresh razor blade. That's an extremely keen, fresh-metal, polished edge, with a polished bevel. It's what you're going for.
Three Finger Test: This is a Chris Carter test, and is very weird. I don't expressly recommend, but neither do I expressly disapprove. The test is foolish and informative. Obviously you have to be very careful using it. Hold the knife by the handle with your right hand (lefties reverse), so that the blade is more or less parallel to the ground. Place the finger tips of your index, middle and ring finger of your left hand against the knife's edge. Lighten up your grip so the edge rests (or almost rests) on your finger tips. Now ask yourself, does the knife feel so sharp you're afraid to slide your fingers at all? Don't slide them, just ask. If you're scared, the knife is sharp. If not, needs more work. The test doesn't become safer the more you use it. I know because I'm stupid.
Forum (Psychological) Test:
If You Gotta Ask Test: The question, "How do I know my knife is sharp?" as posed in a post is presumptive evidence the knife not only needs sharpening, but is significantly duller than when it came out of the box. (Misono ships the knife sharp, but not as sharp as a UX-10 can get.)
PS. I alo recommend reading the Chad Ward article on E-Gullet (which I think you've already done; additionally, it's worth reading the Steve Botoroff e-book -- in fact you may get more from Botoroff. That said, both are dated and too brief. There are better sources of information although you have to pay for them. The best is Chad Ward's book, "An Edge in the Kitchen." I've already mentioned Juranitch. Some people like the Lee book (from Lee Valley), but it's more about tools than knives. If all the explanations get tiresome and all you want is "how to," Dave at Japanese Knife Sharpening has an excellent DVD, as do Chris Carter, and (I think) Korin.
Speaking of videos, Curtis aka C-Dawg of Knife Forum and Fred's Cutlery Forum fame has an excellent video on you tube of him sharpening a Mizuno gyuto. It's just hit this forum as a link. Don't try and sharpen like Curtis until you're already a proficient sharpener. His method is method looks extremely good to beginners because it's not all about "feeling for the burr" and "deburring," uses only one kind of stroke, and relies on counting instead of inspection and touch testing. In other words, it seems as though there's so much less to learn. Unfortunately, shortcuts won't get you where you want to go until you've walked the whole path a few times. I won't post the link, but did describe the "Three Finger Method," read into that what you will.