One, Four, Five!

Here's a way to find out what key a song is in while playing along (and a little music theory)...

Just remember that for any Major key, the first (I), fourth (IV), and fifth (V) notes are always going to be major.  So consider the key of C.

C Scale:     C    D    E     F    G    A    B
Number:     I     ii     iii     IV   V   vi    vii

So we have the One, Four, Five for C major:  C F G

Lets say you're listening to a song, and you can tell it has an A major chord in it.
Using this method, you can quickly find out which key the song is in, and then you'll know which scale to play to fit in.

There are three places this A major chord could fit into the scale, either the first, fourth or fifth position...

1 4 5                   I   ii     iii      IV  V   vi      vii                1 4 5
A _ _   A major (A  Bm  C#m  D  E   F#m  G#m) ==> A D E   is the 1,4,5 for A major
_ A _   E major (E  F#m G#m  A  B  C#m  D#m) ==> E A B  " " " " " " " " " " " E major
_ _ A   D major (D  Em   F#m  G  A  Bm    C#m) ==> D G A " " " " " " " " " " " D major

So from here, you'd want to try to find more chords in the song's progression, and you can narrow down this short list.

Similarly, if all you can find is a minor chord in the song, there will be 4 places in the scale the chord could fit.

Let's say Dm, now we're dealing with 2nd, 3rd, 6th, and 7th positions in the scale (takes a little more time and memorization than the major chord/scale).

2    3 6 7                            I    ii       iii      IV  V   vi      vii                 1  4  5
Dm _ _ _  ==> C major   (C   Dm   Em   F    G   Am   Bm)   ==>    C F G
_ Dm _ _  ==> Bb major  (Bb Cm   Dm   Eb  F   Gm   Am)   ==>   Bb Eb F
_ _ Dm _  ==> F major    (F   Gm   Am   Bb  C   Dm   Em)   ==>  F Bb C
_ _ _ Dm  ==> E major    (E   F#m G#m  A   B   C#m Dm)   ==>    E A B


Practice Tips: 
Try to do the exercise above for another chord other than A major or Dm. 
Try to figure out the chords to a song by ear.

Also,
Play the scale of the key you want.
Then, try to play the chords at each note of the scale. 
Try to mix up which chords are major or minor as you go up the scale, and see how it sounds if you change from the 1,4,5 pattern shown above.  (MAJOR minor minor MAJOR MAJOR minor minor)

Example:
play first the notes: C D E F G A B
then play the chords: C Dm Em F G Am Bm
now see how it sounds to play these chords: C D E F G A B (all major)
or try any other variation from 1,4,5 being major.