the C Major chord
As described in the lesson "Intervals and chords", a chord comprised of three notes is known as a triad. A triad that has 4 intervals between the 1st and 2nd notes (AKA a Major 3rd), and 3 intervals between the 2nd and 3rd notes (a minor 3rd) is known as a Major triad. Thus, the C Major chord is C-E-G.
And, from the lesson "Playing intervals and chords from the C position", you can view this triad as the two two-note chords C-E and E-G combined. Thus there is a white key in between playing fingers.
It looks like this on the staff.
Another way to view this major chord is as the combination of the the C-E chord and the C-G chord. The latter being the Perfect 5th interval. Thus, major chords have a very pleasing sound. Go to your piano and try it yourself. Play both the individual two-note chords C-E, E-G, and C-G as well as the triad C-E-G with both your left and right hands.
You will notice that piano tunes often have the chords on the bass staff to be played by the left hand while the melody notes (the ones you sing or hum) are on the treble staff played by the right hand. This applies to the following tune.
You may know "Brother John" as Frère Jacques which is the original version, a French nursery rhyme. Follow the same guidance as was given for Jingle Bells. First practice the right hand melody and then add in the left hand chords. Here's how it sounds.