How do I know if mine are polarized?

Very easily done. Just look through the glasses at the reflection of any object on a window panel (but not at yourself! you have to look at an angle to the glass). Then, turn the sunglasses around as if they were the hands of a clock facing you. If the intensity of the reflection doesn't change with respect to what you see through the window, they are not polarized. Or you can use as your target image any of the numerous other examples of linear polarization mentioned in this web site: com'on, read on!

I still don't understand, why are polarized sunglasses better than normal dark sunglasses?

Normal sunglasses decrease the intensity of everything by the same amount. Polarized sunglasses can selectively eliminate the reflection from light coming from above the water surface.

Then, could polarized glasses be crystal clear?

Nope, they will always decrease the intensity of unpolarized light by at least half. In practice somewhat more because of losses in the material.  They come in all shades from light gray (only polarizing) to very dark (polarizing plus black tint), and also light sensitive (photochromatic).  You can even find sunglasses with darkness adjustable by the user.

Do polarized sunglasses help see fish and rocks below the water surface?

Yes. First, if there is glare, they help a lot by reducing its blinding effect. Second, even without glare they selectively reduce other reflections from objects above water, including clouds and even the sky (the reflected sky gives most of its blue color to the sea). Finally, light coming from under water is slightly polarized in the vertical plane (polarized on transmission). The end effect is that the water seems darker but more transparent! But remember, it only works if you look at the water at some angle and not straight down.

Does it matter the time of the day?

Yes. Maximum polarization is obtained when the sun is at about 37 degrees from the horizon (in theory 100% polarization at the Brewster angle). If the sun is very low or very high the sunglasses will be of little help in filtering the glare in calm seas. A rule of thumb would be that polarized filters limit the glare from calm waters for a sun altitude between 30 and 60 degrees (but see next question). Anyway, it should be stressed that polarization won't help in looking directly at the sun (except in decreasing the overall intensity of everything by half).

Does it matter the choppiness of the sea?

Yes. When the sea is ruffled the sun reflection becomes the familiar glitter, an elongated pattern of shimmering water stretching towards the sun. Because different parts of the glitter are reflected from different wave slopes, the degree of polarization varies from place to place. In those conditions the sunglasses will also help for high or low suns and the benefit will depend on where you are looking.  As a side note, the width and length of the glitter together with the altitude of the sun can be used to compute the height of the waves without ever getting close to them!

Can polarized sunglasses help when driving a car?

Yes. Those pesky bright reflections of the sun on the cars ahead can sometimes be attenuated a good deal. They tend to be horizontally polarized, thus perfect for vertically polarized sunglasses.  The reason is that the surfaces that you see on the car in front of you (the back window, the trunk door, and even the roof) will be slanted towards you, while the sun will be more or less aligned in the vertical plane through both cars (if not you wouldn't see its reflection from those surfaces). However, if the sun is relatively low behind you, the sun rays will be near perpendicular to the reflecting (vertical) surfaces which won't polarize the light.  The sunglasses will help more with the reflections from the glass than from the metal as the former are polarized to a higher degree.  What about the brightness of the road itself?  That light is also partially polarized, but by scattering (as opposed to reflection).  The direction of polarization will change with the direction of the road with respect to the position of the sun.  The rule is that the polarization is tangential to a circle centered on the sun.  That means that if the sun is in front, behind, or high above, the road brightness will tend to be horizontally polarized and the filter of the sunglasses will provide some help.  However, if the sun is to one side, the polarization will rotate vertically, the more so the lower the sun happens to be.  Of course, if the road is wet you get the same anti-glare power than at sea.http://www.sunglassesreadingglasses.com/product/P11002_Polarized_Glasses_For_Fishing.html

Can polarized sunglasses help in skiing and other non-water sports?

Sometimes yes, sometimes no. The snow glare is not polarized, so they won't provide extra help in that regard (although often advertised for that purpose). But, with the sun high, the air-light (haze + sky) near the horizon is polarized by scattering and the polarized sunglasses can make features far away really stand out (this is used in fire detection). On the other hand, with the sun low the sunglasses could be detrimental looking south or north, as the air-light would be vertically polarized. Other situations can be thought were they would be useful, but remember that one reason they are so good in water sports is that the reflector always remains horizontal!

Can I use my 3-D polarized glasses for fishing?

Not a very good idea.  The filters on those glasses are oriented at 90 degrees to each other, almost always at +/- 45 degrees with respect to the line joining the temples (generally the transmission axis points down towards the nose).  Thus, horizontally and vertically polarized light will be attenuated equally.  In addition, you can get a bad case of dizziness: the left and right eyes may see polarized objects with very different intensities, confusing stereovision and resulting in vertigo (the same effect as produced by the glistening of the snow).  It wouldn't be very kind to give them to your mother-in-law the next time she invites herself to your boat .  .  .