I've been asked two times today, "What key are they playing on this video?" Let me digress for a minute give you Uke Jams' philosophy of song keys: Every song has two keys - the original key, and the key you are playing it in. That's it. Any talk about 'correct keys' is, in our humble opinion, misguided.
When I put a song chart together, I will identify the original key. I try to either find or create a chart in that original key, because playing along with a recording is a great way to check the accuracy of a chart. Once that is complete, I will transpose to a key that works well for the uke and, more importantly, fits my vocal range.
If you're like me and have neither a great ear nor a musical education, how do you find the key of a recording? First, listen to the recording and see if you can identify where in the song the root chord is being played. This chord is typically the one that is played the most often - the song will keep returning to this chord. The most reliable place to find this chord is at the end of the chorus, or the end of the intro. The first chord of the vocal is not as reliable.
Now that you've identified when you think the root chord occurs, get out your uke. Recognize that there are a limited number of possible choices for keys: A, B, C, D, E, F, and G, plus Bb and Eb. There are a few other choices, but they are rare. (Don't forget to include the minor versions of these chords for songs with that minor vibe.)
Every time that root chord comes around in the song, strum one of these candidate chords, and see how it sounds. If you hear a match, you are done! That is your key. This method doesn't always work for me. I wasn't kidding when I said I don't have a great ear!
My second strategy is to guess at the root note of the vocal. As before, this is often the final note of the chorus, and often the final note of phrases throughout the song. I sing along with the recording until that note comes. I stop the recording while continuing to hum the note. I then play a scale on my uke until I find the note that matches what I am humming. Ta da! I have just found the key used in the recording!
A third option is to use an online tool such as Chordify that analyzes recordings and shows the chords being used. I find these unreliable for actually charting a song, but they can be helpful in identifying the key.
Good luck and happy charting.