To put

1.Setzen
2.Stecken
3.Stellen

Can all of these 3 verbs be used to say put something in/on another thing? If yes, which one is more commonly used?

Thank you

Yes, all three of them are correct, but normally, "to put" is translated with setzen/stellen/legen.
Stecken is not that commonly used though correct.

They have different connotations, though.

e.g. "stecken" is mainly used when you put something in something else.

Normally you use "legen" if the object afterwards is lying on something and you would use "stellen" if the object stands (upright) on another thing, eg:
er legt das Buch / die CD / den Bleistift / den Geldschein / den Keks auf den Tisch
er stellt die Vase / Flasche / Dose / den Topf / die Lampe auf den Tisch

er stellt das Buch ins Regal (if it stands upright afterwards)
er legt das Buch ins Regal (if its lying horizontally afterwards)