I hear that in a secret ballot today the House Republicans are very likely to remove Cheney from leadership. But I also keep hearing that most Republicans believe she’s right and are just afraid Trump will see them supporting her. If the ballot is secret, why is it likely to succeed in removal?
No idea, but as an update, it has succeeded.
I see no reason to believe this.
I read it was a voice vote. Does that mean it is not secret?
I have heard many times from reporters that when they talk to Republican House members off the record, they say this.
Maybe they voted with funny voices.
I also heard on the news that they did remove her. But was it secret or wasn’t it?
“Voice vote” means you do the general “all in favor say aye, etc. … the ayes have it” and if nobody with standing asks for a count, there is neither count nor record. To have a secret ballot or a roll call it has to be so asked and seconded.
Per CNN, it was a voice vote, as @JRDelirious explained. It was quick, and as usual for a simple voice vote, there is no record of who voted which way. No one had to go on the record. If a Representative was quiet or mumbled, even other members of the caucus might not be certain which way they voted.
How, prey tell, do they decide whether more were for than against? Is somebody measuring the decibel level of the vote?
If it was a voice vote, then if anyone dared to contest it they would automatically be labeled as a Party Traitor.
Don’t be ridiculous. 
Do you honestly think there were any “nos?” That’s why they wanted a voice vote in the first place.
A lot of Republicans think she’s right about Trump but think she should shut up about it for the same reason that they themselves are shutting up about it.
Fear?
Avarice.
50/50?
Bottom line is he has a huge following among the RP base. Constantly harping him undermines the party.
The idea is to keep quiet and hope he moves to the back burner and fades away and/or dies or whatever.
Pretty much. The chair just decides whether there were more “ayes” or “nays”. At that point, someone can (depending on the specific rules for that specific forum) move for a vote by an alternate procedure (such as a roll call or vote by ballot). If they get a second to the motion, the vote must then be held by the alternate procedure.
This is a procedure that can be abused. A chair can ram through a measure by voice vote, declare the winner, and then gavel the vote closed before anyone has a chance to object.
Kangaroo Congress.
Or, as I previously stated, the chair can just make a declaration knowing that any objection will be seen by the group as a betrayal of the party.