Major and Minor Keys

You can't tell from the key signature because A minor and C Major are the same, as are C minor and Eb major etc. Download some old scores from IMSLP with "Major" or "Minor" in the title. Look at the key signatures and listen to the pieces. Eventually it will click.

To further complicate things, there are various modes described that are not strictly major or minor but have descriptions such as Dorian or Mixolydian - you need to look up a music theory website for discussions on this.

Generally the last chord (and/or melodic note) of a section will help determine the key.

Here are a few examples:

• If the key signature has two sharps and (excluding "pickups") the last chord is D major or the last note is D the key is probably D major (the Ionian mode.)

• If the key signature has two sharps and the last chord is Bm or the last note is B, then the key is probably B minor (the Aeolian mode.)

• If the key has has two sharps and the last chord is E minor or the last note is E the key is probably E dorian.

• has two sharps and the last chord is A major or the last note is A the key is probably A mixolydian.

But there are lots of compositions that start on a note that differs from the key. Consider Mary Had a Little Lamb. Pachebel's Kanon in D starts of F#. So it's better to rely on the final note or chord. And even better to rely on the concept of tonal center, because in certain styles of notation (like fake sheet) the melody and final ending might serve to lead back to the head, so the last chord is likely the V of the key; so it this type of form the last chord written is not really the final chord.

There are lots of variables that contribute to the sense of tonal center, so there's no definitive formula or answer for the key of certain pieces. For instance a piece may have changed key by the time it completes a section or its entirety, and in such a case the last note only represents the tonal end of the piece. And sometimes the melody doesn't end on the tonic. But the chord usually does. For simple songs, just compare the last chord/note to the key signature, as shown in the chart of the modes below.

If unfamiliar with the modes of the major scale, study up on them. A good explanation (of which there are few) will help clarify the notion of tonal center and key signatures.

Here's an example of a key signature and its modes. The signature with two sharps is generally thought of as the D Major key signature, or the B minor key signature. But it can be any of the following: iIf the tonal center is D it's major; if the tonal center is E it's Dorian, if the tonal center is F# it's Phrgian ... probably better illustrated in a chart:

     D Ionian (same as Major)
     E Dorian
     F# Phygian
     G Lydian
     A Mixolycian
     B Aeolian (same as Minor ... and the relative minor of D major)
     C# Locrian

scorster

First chord, last chord ... might work in many cases, but is very unreliable in general.

I would propose combining intuition with knowledge of key signatures:

Look up the key signature. For example, one sharp sign: G major or e minor. Listen to (a part of) the piece, for example the first bars or the last bars. Try to hum or play the note on which the piece would end to feel resolved. If it's either G or E, you might have found it. If it's something else, the situation may be more ambivalent - as others already wrote, there are many more modes besides major and minor key.

Second method, requires less intuition: Minor keys usually have some different accidentals. e minor has one sharp in the key signature, same as G major, but in order to resolve on e, in classical music you can also expect there to be D sharps leading up to it, and possible C sharps to get to the D sharp without a jump.

It all strongly depends on which time period and style we are talking about. In baroque time, you can pretty much just look at the final note to find your answer. In romantic era, a piece could deliberately end vague in order to express some emotion (although still uncommon); also, other modes besides major and minor become increasingly important throughout the 19th century. And in 20th century popular music, chord progressions are very often based on modes other than major and minor.

By far the best way to learn this in through actually playing and listening music in different keys. One can't tell you blue looks like; we can only tell you to look at blue things and ask you to see for yourself what they have in common, and hope that the connection is made. Same for telling the difference between major and minor, or identifying the tonic of a melody, etc.

But FWIW, the trick of listening to the last note / chord is definitely useful a lot of the time (but not always - I'd practice first using really simple songs to get a feel for this). The first note/chord not so much - it's only going to be the tonic "some" of the time and is really just as likely to be something else.

You wrote:
When I use a key for a particular piece I need to determine if it is the major or minor for that key signature.

In addition to all the fine advice given here...
An interesting way to "get a feel" for major and minor through actual listening is to compare a simple melody written in parallel keys.
Here's an example:
Major-minor.mscz
Simply listen to the example as two separate tunes and compare the sound and mood of major compared to minor. Let your ear judge the difference.

Regarding relative keys, (e.g., C major - A minor, which share the same key signature) see:
https://en.wikipedia.org/wiki/Relative_key

Regarding parallel keys (e.g., A major - A minor, which share the same tonic) see:
https://en.wikipedia.org/wiki/Parallel_key