Breakdown of Setzen Sie sich doch zu mir!
Sie
you (polite)
Sie is the formal version of you which you we use with everybody except close friends, family or children. Once we get more friendly with people, we might offer them or they might offer to us to use du instead.
mir
ich - dative case
ich - mir
du - dir
Sie - Ihnen
du - dir
Sie - Ihnen
sich setzen
to sit down
important: this is a movement towards a direction (down) you are standing and moving into a sitting position.
zu
to; at
doch
why don't you
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