The precise rules for dealing with thoughts are not recorded in standard grammar and usage books. There are opinions on how to do this based on current trends, which may become dated in a few years. One of these is to use italics without quotes to distinguish internal thoughts. If the writing is from the third person point of view, there should be no need to use “he thought” or “she thought.” For example:
Frowning, his mother motioned for him to come. So, Garth trotted up the tenement stairs. She just wants me to stop talking to those guys because they’re not “our people.”
In this case, there is no need to insert “he thought” before the italicized words as this phrase is obviously going through Garth’s mind. The quotes are not spoken but used to emphasize words his mother would have said. But, I could have easily written “So, Garth trotted up the tenement stairs thinking…” It would not have made any difference. It is something that I normally do not do. But, I’ve had beta readers ask, “Who is saying this?” when I didn’t.
There are different ways to deal with protagonist’s thoughts written in first person. One is to not differentiate thoughts from the rest of the text. This view is defended by the view that the entire story comes from the thoughts of the narrator. The difficulty is that not all conversations are vocalized. What if a voice speaks inaudibly to the main character? The text should indicate the distinctiveness of this kind of thought. Usually, italics without quotes are used for the actual words.
I slipped into the worn red rock crevice to check out the size of the cave. Do not go any farther. I twisted around with an involuntary shiver at the words.
What if a protagonist thinks in words but does not actually utter them during a conversation? This thought may be in the present tense while the story is related in the past tense. Again, I use italics to distinguish this thought.
“Hello Patricia!” I called from the open door, but she turned her head and said nothing. Okay, don’t talk to me if you don’t want to.
What if the protagonist recalls words that other people said while he is thinking? The memorable phrase was spoken aloud in the past. But, at this point in the story, the point-of-view character is remembering them. I use italics and quotes to separate these words, just as I used for the words that Garth would remember in the first example.
In places other than the United States, single quotes may be used for thoughts. Within the U.S., they are used for emphasis within a spoken conversation, or when a character quotes someone else when speaking. Some authors use italics for emphasis when speaking when they should be reserved for use of foreign words in conversation. However, there is no requirement to put foreign words in italics. This way of distinguishing foreign words does not work well if you use a lot of them. Your major concern is to be consistent in the way you use italics and quotes.
Finally, do not be afraid to let the readers know whose head they are in. The reader should not have to struggle to tell who is thinking and who is speaking aloud.