The chord that is used most is a diminished seventh chord, not a three note chord.
Here's how is has to be used. 1,3,b5,bb7. For example, key of C: C,Eb,Gb,Bbb (A)
It is built on minor 3rds. There are two practical ways of using it. One is to play it the way you would play a major chord, (the same name). C diminished seventh for example.
The other would be to play it a half step higher, C# diminished seventh for example.
The best approach is when you are learning a song, the sheet music in early pop music will contain the name of the diminished seventh that you need.

It gets complicated theoretically because a diminished seventh chord is built upon a dominant seventh flat nine chord. If a dominant seventh flat nine is spelled out, 1,3,5,b7,b9 as a five note chord, the top four notes of that chord will become a diminished seventh chord.
Example: C,E,G,Bb,Db is the C7b9 chord. E,G,Bb,Db becomes the diminished seventh and takes the name E diminished seventh. (The C is called the "generator" of the diminished seventh chord.

The most practical way to use it is to just take the name of the chord given to you in the sheet music.

Now on the accordion, you only have the three note triad in the bass. You have to add the other note with the right hand on the piano side or suggest it with the playing of a scale or arpeggio.