Well if a song is in C and you play over the song with the C major scale, everything will sound good.
Now it dosnt meen you have to stay there. Sometimes going out of the scale intentionally, at the right moment, can add nice tensions in the song.
But generally, when beginning, your better of staying in the key (in the scale). Later on you can bend/break the rules.

Generally a song will start or/and finish on the key/root. You can also use your ears. If you listen to the song closely, you will ear a note here and there that sounds like its concluding something (melody/lick/riff, whatever).That's the root.

You can also get/find the chords of the song and that will give you the key.
Lets say you have a song with a chord progression that goes :
C#m, A, Bm

Using the Diatonic Major or minor chords formula you can find the key of the song.

Major diatonic chord formula:
Major, minor, minor, Major, Major, minor, diminished or I, ii, iii, IV, V, vi, vii
(Ex: Key of C the diatonic chords would be....C, Dm, Em, F, G, Am, Bdim)

Minor diatonic chord formula:
minor, diminished, Major, minor, minor, Major, Major or vi, vii, I, ii, iii, IV, V
(Ex: Key of Cm the diatonic chords would be....Cm, Ddim, Eb, Fm, Gm, Ab, Bb)


Let's take the progression's chords and place them in order using the Minor diatonic chord formula and placing the C#m as our first chord.
1st chord would C#m, 2nd chord would be D#dim, 3rd would be E, 4th F#m, 5th G#m, 6th A, 7th B....errrr....we got B minor in our progression and not B major so it cannot be in the key of C#m.

Lets try with A major using the major diatonic formula.
1st is A, 2nd is Bm, 3rd C#m, 4th D, 5th E, 6th F#m, 7th G#dim. Everything works so the song is in A.

Lets try with the 3rd chord just for fun. Bm with our diatonic minor formula.

1st Bm, 2nd C#dim....errr....we got C# min, so it can't be in the key of Bm.

It might seem complicated and long but all this becomes 2nd nature eventually. I hope this helps you.