Pôr-se a caminho = começar a caminhar
Passado:
Eu pus, você pôs, nós pusemos, eles puseram
The key to understand what is going on: The reflexive of "we" is "nos" but if you have to write "we put ourselves" then it'd be redundant or weird to write: " pusemos-nos ", so that's why it is shortened in order to sound good "pusemo-nos"
mos-nos (weird)
mo-nos (okay)
It'll happen everytime you have this kind of construction!
We spoke for one hour:
Falamo-nos por uma hora
We hugged a lot before the departure:
Abraçamo-nos muito antes da partida