How do you figure out what singing range you're in?

You need to have a trained vocal instructor listen to you sing for a while in a number of settings. This person will listen for where your voice tends to get comfortable.

There are several ways of dividing the human vocal range. Here's the most common (high to low):

soprano
alto
tenor
bass

Usually the last two are sung by males and the first two by females.

Another way:

Coloratura Soprano (sometimes not considered different than soprano)
Soprano
Mezzo Soprano
Alto
Contralto (sometimes not considered different than alto)

Countertenor
Tenor
Baritone
Basso

Very small.... I think it's comfortably about... 2 octaves? From the E below middle C to the E two octaves up from that. That's about right I think.

About two octaves, from the F below the bass clef to the F above the bass clef. I’ve actually been known to get down to E while sick, but of course the top of my range is also lowered. ;-)

Well the way most people go about doing this, is by just singing some simple scales. Start at the lowest not you can possibly reach, and then go up the scales until you reach the highest note you can get out nicely. this should give you a little bit of an idea of where you stand on the scale of soprano, alto, tenor, and bass. If you really can't figure it out by yourself, ask a friend to listen to you and help you go through the scales. Hope it helps!!

The best way is to have someone who knows these ranges listen to you sing and have them determine your status.

This is how the ranges work:

Bass is as low as it gets
Alto is moderate
Tenor is higher
Soprano is highest in pitch

I believe there are also a few others in between, but that's about it.
For the amateur, telling the difference between tenor and soprano may be very difficult, which is why again, I recommend having someone evaluate your voice and determine its range,

Firstly, there are several different ranges. For men, there are three typical voice types:

Tenor
Baritone
Bass (or Basso)

For females there are also three:

Soprano
Mezzo-soprano
Alto

All singers can be classified under one of these groups, but just because you find yourself in one group does not mean that you cannot sing in another ie. most sopranos can also sing mezzo and alto.

Not that the following does not apply to all singers, as each voice is unique.

For females:

For the female range, sopranos generally feel most comfortable from middle C to about two octaves above middle C.

Mezzo sopranos generally are in their element between the C above middle C to a low A.

Altos usually are able to sing from G to about an octave below middle C, but sometimes are comfortable up higher.

For males, as follows, but please note that falsetto (very high, or woman-imitation singing voice does not count.):

Tenors usually are comfortable in the range of a mezzo-soprano.

Baritones generally find themselves in the range of an alto.

Basso are typically able to sing from about an E below middle C to anywhere below that - possibly two octaves down.

A simpler way, if you aren't inclined to piano scales, is a rough rule of thumb:

If you think you sing high, you're soprano/tenor.

If you sing low, you're alto/basso.

If you like to sing in the middle you're mezzo/baritone.