1
If you use a descriptive term to refer to the researchers instead of their names, put a full citation where you would put it without that descriptive term:
It has been determined that bla bla (John et al., 2023).
becomes:
Researchers from the University of Michgian's Department of Computational Analysis determined that bla bla (John et al., 2023).
2
If you refer to the authors by name in text, but your reference doesn't exactly look like the citation would look, use a full citation and put it where it would go without the names of the authors in text:
Robert John from the John Writing Institute and Peter Williams, professor at the University of Chicago department of creative writing, have determined that bla bla (John & Williams, 2023).
3
If you refer to the authors exactly by the names as they would appear in the citation – that is, without first names and without additional descriptive phrases –, put the citation immediately after the names of the authors:
It has been determined that bla bla (John & Williams, 2023).
becomes:
John and Williams (2023) have determined that bla bla.
Note: In scientific writing, never use the first names of authors that you cite in text. Only use last names. Use first names if a person is the subject of your research, e.g. if you study a historical person or the work of an author.
In the following citation, Robert John is an eminent scholar and I make a remark about his contribution to the field:
Robert John has significantly contributed to our understanding of how writers write with his research into the psychology of writing. His first publication, How Writers Feel when They Write (John, 1950), changed our view of writing fundamentally.
Note how I switch to last name and year when I cite that distinguished expert, although his work as a whole is the subject of my paper.
4
Do not ever write "et al." in text! Resolve that abbreviation. "Et al." is short for "et alii", "et aliae", or "et alia", and means "and others".
It has been determined that bla bla (John et al., 2023).
becomes:
John and colleagues (2023) have determined that bla bla.
Use words similar to colleagues to translate alii.
Note: A descriptive phrase, such as "researchers from the University of Michigan", is not an adequate in-text resolution for "John et al."! See the examples above for that.
5
The year should follow the in-text names of the authors if you add a description of who those authors are:
John and colleagues (2023) determined that bla bla.
becomes:
John and colleagues (2023), of the John Writing Institution, determined that bla bla.
But I would prefer something like the example under no. 2 above:
Robert John and a team of researchers at the John Writing institute have determined that bla bla (John et al., 2023).
This better explains who the "et al." are and reads more elegantly than the preceding variant, in my opinion.
Note
English is not my mother tongue. There might be stylistic, grammatical, or orthographic mistakes in my examples.