As cosplayers, we often have to change our eye colors to match the (often wildly improbable/impossible) eye colors of the characters we depict. A good set of colored lenses can make a huge difference! I didn't see any topics about this (if I missed it, sorry, and feel free to move this as appropriate), but I did see a question or two and figured I'd take a crack at it. I am by no means an expert (or optometrist!), so chime in with any other experiences or considerations I may miss!
Power is the capability of the lens to compensate for you being near- or far-sighted. Can you see things close up, but not far away? You're probably near-sighted! (Join the club, my friends.) If you have a large enough deviation from the 'standard' of what should be visible at 20 feet, you probably already have vision correction, perhaps in a pair of prescription contacts, or maybe in glasses. Power is often not the same in each eye and may vary over time.
If your eye just isn't a perfect ball shape, you may have a condition called astigmatism. (Again, welcome to the club!) It often creates starbust patterns around light sources, and may multiply the edges of objects, which is especially troublesome for fine-detail tasks or at night. Astigmatism may be very mild or very severe, and is independent of power. You may have no need for a powered lens, but your astigmatism may require correction. Special lenses are required to correct for astigmatism (typically called toric lenses, these usually have a thicker or heavier edge so they rotate on your eye when you blink so they are always right side up). As with power, astigmatism may vary between eyes, or over time.
Seeing the Optometrist
Sorry, fellow citizens of the U.S! It is completely mandatory to see an optometrist to get contact lenses in the States. While it sucks, this rule is in place for some good reasons. You can honestly blind yourself temporarily or PERMANENTLY by not exercising proper lens care and optical hygiene. Additionally, having an incorrect lens shape can cause problems even if you have no vision correction (lenses with no correction are called Plano). Besides, some medical conditions manifest early in the eyes, or impact the eyes preferentially, so it's worth it to have the doctor check out your eyes--no one wants to go blind for a silly reason like an undiagnosed glaucoma, or chronic dry eye, or a detached retina (though that one is an emergency situation, so hopefully you all would notice and get that looked at immediately!). So please don't buy lenses from anyone willing to sell them to you without a prescription. Can you get them? Sure. And they'll probably be just fine. Still...I for one wouldn't gamble with something like my vision. Similarly, follow the guidelines provided by your lens manufacturer about how long you can wear them and when to replace. Wearing lenses for too long can literally suffocate your eyes, which get a lot of their oxygen directly from the air. So they grow extra blood vessels. Into parts of your eye that have no business with blood vessels. Yuck. Seriously.
So...now that the health and safety stuff is out of the way...
Lenses come in practically any color you can think of. Some vendors will even custom create lenses for you, if you need a special color or pattern. Some are engineered for full color change--they have solid color from the outer edge of the iris (called the limbic ring) to the edge of the pupil. These are the ones most likely to look unnatural, especially if your pupils are contracted, as the edge between your eye color and the lenses may be readily apparent. But if you're looking for a really dramatic change, especially dark to light (your eyes are brown and you need light blue), these are the way to go.
What if you want something a little more natural looking? Some lenses are speckled with color so they let your own color through. Some are speckled all over--you have to be careful of these, in case the colored area is larger than your iris, as you really don't want a speck of whatever color in the middle of the white of your eye (the sclera). They also may be too subtle a change, especially on dark eyes. Others tend to have a dark limbic ring and speckling inside so they clearly define an outer edge (typically quite larger than most people's irises are), but shade into your own color toward the middle. These tend to look the most hypernatural, though you may find the limbic ring a little weird at first, especially if yours is naturally pale or thin.
Some special lenses have special applications. For example, if you need to look 'blind' with milky eyes and an invisible pupil, some lenses are made to achieve this effect. Be careful, as some really will blind you while they are in! Most have a tight mesh pattern that you can see through, but which other people only notice if they're very close and paying attention to it. Some of these lenses also come in colors, in case you need all over color from the limbic ring inward.
There are lenses that cover the sclera partially or completely--think about solid black eyes with no white visible, or eyes with red whites. These are very difficult to put in and handle, and should be used with care. They are also commonly really uncomfortable, but if you ever have PAIN when using contacts (of any sort), STOP! It shouldn't hurt if you're doing it right.
Then there are lenses with UV-reactive colors--they glow under black light! Generally these can be treated like normal contacts, but they typically only come in solid colors or with iris effects. You will want to be careful using these if you want to wear them in the day, too, as the color under full light often varies a bit from that under black light.
And finally there are a slew of prints and iris effects. Iris effects are things like appearing to give you slit or diamond pupils, but they're really just a type of print. Prints vary from geometric shapes, to text, to symbols of all sorts (and yes, iris effects). These are also treated just like normal contacts. The trick is in finding the pattern you need or want. Some vendors will custom make these for you, if you cannot find a pair that suits your need, but expect to pay a whole bunch for them.
Colored lenses are always more common in plano. If you need a prescription set, you will have more limited choices and pay more for them to boot. There are very, very few options for toric lenses in colors, and fewer still with fancy patterns. Some people will layer lenses together to get around this, wearing a prescription lens with a colored one on top. This is a pretty terrible idea. It suffocates your eyes more quickly, provides an awesome spot for bacteria to grow (between the two lenses), and the contacts may shift against each other, resulting in scratched or torn lenses or lenses that displace relative to each other, leaving you blind. You can sometimes get away with wearing a powered lens and ignoring your astigmatism, so long as your astigmatism is mild and you're not trying to do anything like drive, shoot, or read. Or bring a pair of glasses to use while you're not being photographed. I used to use the glasses method, but I talked to my optometrist and he was able to tweak my prescription a bit to let me function with just the powered lenses. I just won't drive, and don't ask me to read anything more than arm's reach away.
So...some places to get lenses.
1800contacts.com - obvous, but the do have a ton of lenses. Just don't expect really exotic patterns.
lens.com - another huge site for lenses, but again, don't expect all the crazy patterns.
your optometrist - believe it or not, you actually can sometimes get some really great deals from your optometrist, and in my experience they are usually interested to hear about what you're doing, so don't be shy!
cosplaysupplies.com - a great site for all kinds of stuff, from fabric to pre-made props, to wigs, they also carry lenses. Some are even custom colored/patterned! Unfortunately, they won't sell to the U.S. Fortunately, they have a sister site that will, and that is...
cosplaylab.com - lots of lenses and available to U.S. customers, also with custom hand-painted lenses available. I have had good luck with them.
pinkyparadise.com - another huge selection of lenses. I know someone who loves them. They have lots of plano, but prescriptions are a little anorexic.
foureyez.com - I used to love their stuff--until they decided they cannot sell to the U.S. Maybe they've changed again, but...
Anyway, far from an exhaustive list. Feel free to jump in and add any other sites or information that might be useful.