The best way for testing if a knife is sharp enough is usually to try and use it for its intended purpose. Assuming you have an idea what you're doing, you will quickly find out.
There are, however, several test which can be used to test a blades sharpness. My favourite, which I use on my straight razor from time to time, is the hair test. Get one of your hairs, hold it from the root end (I don't actually know why you're supposed to do this, but it's what I've been told to do, and so what I'm used to doing - I suspect it's so there's less weight bearing down on the edge), and gently move the hair down from about an inch or so above the blade. If upon contact with the edge, you hear a pleasing little *zing* and stand with a shorter hair in your hand, you have a very sharp blade. A blade that is able to cut the hair if you sort of pull a bit down with your hand as the hair touches it is still quite sharp, and I have no problems shaving with one that cuts the hair if I do gentle swings directed at the hair either.
The fingernail test is another one. Wet your thumbnail (it is the thickest and toughest nail on your hand, and so is the safest, though I have never experienced cutting very deep into the nail), for example by licking it, then gently slide the blade of the knife over it. The most important thing you'll learn from doing this is whether your edge is alternating between dull and sharp, or have small chips in it. You'll be able to feel the change between dull and sharp, though you need some training to judge how sharp it is. I can't really do this. Chips in the blade will tug on your finger, and depending on intended use, can be really detrimental to its function (you can get away with pretty awful chips for some uses, but, say, the aforementioned straight razor will probably be hell to use - no direct experience, really, just guesstimating).
You can also use the other side of your thumb, sliding it across the edge (not along it!) back and forth to judge sharpness. You'll feel chips this way as well, though maybe not the smallest ones, but again it takes some training to accurately judge how sharp the blade is. Judging if a knife is sharp enough for kitchen use isn't too hard with this method, I find, but I can't feel if an edge is keen enough to shave with.
The tomato test is really quite nice on kitchen knives. It's a good gauge of sharpness for their use, and is done by trying to slice a tomato with the knife without using any pressure. Just lightly touch the knife to the tomato and move it a short distance - if the skin is cut through, the knife is sharp.
As a sort of postscript, I want to mention that there are a number of different visual tests, possibly somewhat more objective than most of the above. I suspect these are better observed than explained, so if you're really interested, go check out Youtube for something like "straight razor sharp test". It should actually get you the video I first saw about these visual tests.