The Nashville Number System is an efficient and quick way to determine the key of a song, with several ways we can do this.
I often times like to think of a detective searching for clues when I'm looking to determine the key of the song. A detective with one clue might have a hunch. However, with a second, third, and fourth clue we can start narrowing down exactly what key we are in. For music, these clues come in the form of notes and chords. One clue that is apparent and often times correct is the first and last chord of a song. Often times but not always this will be our one chord and key, given that there isn't a "fade out" so we can't hear the last chord.
Remember the difference between the "key of" and "feel of" in a song. The song can feel like you are in the key of C if you're playing C, F, and G chord forms. However, if you have a capo on your guitar while you're playing these chords, you'll actually be in another key.
Use the chord matrix against some of your favorite songs and see if you can't determine the key by just comparing the chords that appear. Remember, each chord and note is a clue that points to a particular key.