Actually, dew can form at any time; it just needs the right weather/temperature patterns to make it happen.  However, nighttime is usually the primary period when the factors that cause dew to form are just right. Although, as an example of when dew can frequently form when it’s not the morning, I remember MLB superstar Ichiro Suzuki mentioning once in an interview that dew often forms on Safeco Field in the summer evenings during games (that typically run from 7pm-10pm-ish).  This is why, if you watch, you’ll see him periodically run his fingers through the grass to see if it has become wet from dew since the last time he checked.  If so, he factors that into how he might play throwing someone out. (If a ball that touches the ground before he gets to it is going to be wet when he picks it up, it makes it slippery; so depending on the game time situation, he may decide to be more conservative on throws back in to the infield, in case the ball slips when he throws it.)

In any event, to answer your first question of what causes dew, air holds a certain amount of water vapor in it.  How much water it can hold depends largely on the current ambient temperature (as well as barometric pressure, but what’s more important for this discussion is temperature).  The higher the temperature, the more water vapor air can hold.  This is why when you’re in places that are really hot, particularly when near a large body of water, you’ll often feel “sticky” due to how much water vapor the air is capable of and currently holding.

In the evening and throughout the night, there are many things outside that aren’t able to strongly conduct heat from deep in the ground or they otherwise radiate heat faster than they can absorb it, like grass, cars, many metal objects, lawn chairs, etc.  The temperature along the surfaces of these objects can eventually cool past the “dew point” (the temperature at which, given the atmospheric pressure and humidity, the air can no longer hold all the water vapor it contains).  Once this happens, water from the air will condense on the objects, forming droplets.

This is pretty much the exact same process that causes water droplets to form on the outside of a glass of ice water.  The ice inside cools the glass and air around the glass, lowering the amount of water vapor the surrounding air that’s in close proximity to the cold glass can hold, thus causing water droplets to condense on the glass.

Bonus Facts:

• This same basic process to how dew forms is how frost forms, though in this case, the water goes directly from a gas to a solid state, a process known as meteorological deposition.  When this happens, there is so little water vapor in the air that the dew point drops to below freezing and thus it is no longer called dew when it forms, but rather frost.
• The reverse of deposition (the process where gas turns into a solid) is known as sublimation.
• Another thing you might occasionally see that looks very similar to dew, but isn’t, is something called “guttation”.  This is where plants are getting too much water and so pressure from the absorbed water in the roots pushes up and out of special leaf edge and tip structures.  This almost always happens during the daytime, as the stomata are closed at night.  This water also often contains sugars and minerals, unlike dew.  Besides the time of the occurrence, you’ll also be able to tell the difference because once the water evaporates, it will often leave behind a faint white substance on the leaves from the remaining sugars and minerals.
• Dew is more likely to form on clear nights with a decent amount of humidity in the air near the ground, particularly after a warm day.  Usually it’s best that it isn’t too windy either, as this can transport warm air to the cold surfaces, warming them up as well as providing air that can hold more moisture.
• Various researchers have worked to create dew condensers to harvest dew for use in desert regions and other areas where water is scarce.  Researchers at the Indian Institute of Management Ahmedabad, have created one such device that can harvest close to 200 liters (about 53 gallons) of water per night during the “dew season” in their region, which lasts about 8 months.
• The word dew ultimately comes from the Proto-Indo-European root “dheu-“, meaning “to flow”.