Birthday Candles
This is probably the best-known wishing method, and also the strongest, as it only comes once a year. This is not a wish you should waste on something like "I wish the guy at the coffee shop would remember my extra foam tomorrow."
With the cake in front of you, take a deep breath. The older you are, the more air you will need. Make your wish while you are still holding your breath. Now, blow. If you get all the candles blown out with one breath, you wish will come true. It is acceptable for very small children and very old people to receive assistance.

Falling Stars
This is a nice wish, because multiple people can wish on the same star.
All you have to do is see a falling star ("meteor," for the more scientifically minded), and make your wish. The only rule is that you must see the star yourself. A good time to get a wish like this is during a meteor shower.

The First Star
This happens every day, so it's good for your more mundane wishing.
When you see the first star that appears in the night sky, recite this rhyme:
Star light, star bright
First star I see tonight
I wish I may, I wish I might
Have the wish I wish tonight.
Then make your wish. You get even more mojo if you watched the sunset first.

Wishbones are found in any whole cooked fowl. Generally, the larger the bird, the stronger the wish.
This wish takes some preparation, as you have to let the wishbone dry out before using it. Overnight is usually good enough, although if you're in a hurry you could put it in a low oven for a few hours. Once the wishbone is dry, get someone else to hold one end while you hold the other. Close your eyes and make a wish, then pull apart the wishbone on the count of three. Whoever gets the larger piece has their wish come true. In the extremely unlikely event that the pieces are equal, both wishes come true.

As far as I know, this is only a tradition in my family, but I feel that it is only fair to share and enjoy.
When you eat a slice of cake or pie, cut off the point before you start eating and save it for last. When you eat the point, make a wish.

Necklace Clasps
When the clasp on your necklace is turned all the way around to the front, someone else can turn it back for you and tell you to make a wish.
This doesn't work if you do it for yourself, so it's a good idea to train all your friends to keep an eye out.

When an eyelash falls out, blow it off your fingertip and make a wish. Don't pull them out, though, not matter how desperate you are--all that will get you is funny-looking eyelashes.
Some say this is like the necklace wish in that only someone else can do it for you. See eyelash wish for details.

This is a very difficult wish to make come true, so I would suggest trying it out with something that's not very important until you get the hang of it.
Get a dandelion that has gone to seed; that is, the soft white puffy kind. Make your wish, then try to blow all the down off it in one breath. If you get it all off in one puff, your wish will come true.

I think this only works with man-made bodies of water, such as wells, fountains, koi ponds, log flume rides, and so on. If anyone has gotten results with rivers, lakes, the Marianas Trench, etc., let me know.
Take a coin of any denomination (bigger coins make stronger wishes). The coin should be of the currency of the country in which the wishing water is located, unless you are somewhere like Solvang or Chinatown, in which case it's probably better to use the currency of the country you are "supposed" to be in.

White Horses
If you see a white horse, you can make a wish, but only before you see its tail.

LaggedyAnne says: "Iif a ladybug lands on you, say 'ladybug, ladybug, fly away home,' and if it flies off you wish!"