How do they make sure the signals being sent by Voyager get to earth in a state we can read?

Every datacom (even on earth) has some sort of error correcting mechanism. In the early days they used parity checking, but now there are far more sophisticated ways to calculate a numeric value for each packet (punch) of data that is sent, and when it arrives, the receiving computer calculates the value as well. If the two numbers match, then the transmission is assumed accurate and is used.

There are also mechanisms to retransmit packets of data which show errors (i.e. the numbers don’t match) – again, to be sure that what is coming is correct.

It’s the same general principle used on your cell phone, your internet connection, and even your telephone, except much more sophisticated.