1) Scout a province with Mars Ore Deposit
2) Acquire that province
3) Click on the Mars Ore Deposite in that province
4) Pay the necessary amount of Credits to start the exploration
5) Wait until the exploration is over
6) Either negotiate successfuly or fight and win
Done - you get some Mars Ore.
Now do all of that again, and again, and again, until you have enough Mars Ore...