Does one have to say something to a false god in order to be liable?
Well clearly not when it comes to the four services or for עבודה כדרכה (service according to the way it is usually served e.g. throwing stones at an idol that that is its way of being served.)
That is five things. But there is a sixth way of being liable for idolatry--and that is to accept it as ones god. Does that need a word?

In tractate Kidushin pg 50 it says דברים שבלב אינם דברים words in the heart are not words.
There is a Tosphot in Ketubot  that deals with the difference between words in the heart are not words and the conditions of the children of Gad and Reuven when they came into the Land of Israel. They had to make a condition that had in it "sic et non" (yes and no). "If we go up and make war with the inhabitants then we will inherit our portion. And if we do not go up and make war then will will not inherit." I forgot that Tosphot.
This is also relevant to what you find that women go up to a certain point in sexual activity and then  do not want to go further. That is very common. Even in cuddling. And now in collages women bring rape charges not because they said "no" but because they did not say "yes." "Yes" means "yes."

But what I wanted to mention here is that Shelomo Ben Aderet [the Rashba] said that words in the heart are not words only when the contradict one actions or spoken words.

Now all this is just preliminary. I have not yet studied the actual Gemara that I am tried to deal with here with my learning partner. That is the Gemara in Sanhedrin page 63 a.
But just off hand we know already that for truma [the tithe given to the priest] and sacrifices to the Temple that words in the heart are words. But that is OK. The Talmud already said in Kidushin that these are derived from two verses and so we don't learn from them a general principle. שני כתובים הבאים כאחד אין מלמדים.
This the Rashba answered in his way that there the actions and words in the heart correspond.
But then why would the Gemara have to learn this from special verses? Rav Shach (Elazar Menachem Shach) said that there is a difference when something is accomplished by the word one speaks. For example getting married. קידושין. We know from verses in the Bible that one has to say something like, "Behold you are married to me by this ring according to the Law of Moses and Israel."

And there are places where we don't need words except to show intention--the words themselves accomplish nothing. In Yeshivish jargon they don't make a "חלות"

According to this in idolatry one would not need words to be liable.

If one does not need a word to be liable then the Mishna in Sanhedrin pg 62 side b is hard to understand. "המקבלו כאלוה והאומר לו אלי אתה" One who accepts it and says to it you are my god. is liable. What does that mean? You need both or either? Et or vel?

In any case the Talmud goes into the question, "Why is saying a word liable?" It seems to take it as a given that that the mishna is all one clause.

Does this apply to people? Can people be idols? Well obviously according to the Rambam in the 13 principles of faith. [Not the redaction the Sidur but in his actual commentary to the Mishna].
But what you see in the Gemara in Sanhedrin 63 is that joining something to God is also a problem. To Rabbi Shimon it is straightforward idolatry. To Rabbi Meir it is not. In any case it seems to be a problem to Rabbi Meir also.

In the tithe [truma] to the priest if one puts his mind on one side of the wheat stack to call it the tithe"truma" he is allowed to eat from another side. There is a special verse to show this. So there words in the heart are words. But in a case where one sold something with intention to go to the land of Israel and was stopped from doing so--but he did not say anything about that condition--then words in the heart are not words. The sale goes through.
In marriage if she says, "You are married to me," and gives him a ring, she is not married. Only the man can say, "You are married to me." If she says give money to so and so and I will be married to you by that, she is maybe married. It is a doubt.  Because in marriage we need a word to make an act.