I want to introduce the findings of a case study in my report, but it has four authors and I would like name them in when introducing it.
What would be the best way to do this, or is the below perfectly acceptable?
Andria A, Paul S, Derek B and Howard C provide an interesting insight in their case study...
How to handle this depends on your field. If your field has a notion of first author, then "[name of first author] et al." is appropriate. In fields like math that use alphabetical ordering, I'd strongly recommend naming all the authors, since "et al." could be read as diminishing the credit later authors get. I would not be happy if my name disappeared into an "et al."
The sentence "[last name of author 1], [last name of author 2], [last name of author 3] and [last name of author 4] provide an interesting insight in their case study..." sounds fine to me. (I.e., the same sentence as in the question, except that I assume "Andria A, Paul S, Derek B and Howard C" are just stand-ins for the actual names, and not actually a proposal for how to format the names.)
This is completely dependent on your citation style. Two examples:
For APA, if there are only two authors, cite both each time; if there are between three and five, cite them all the first time then cite as "First et al., 2014" in subsequent citations; if there are six or more, use "et al." every time.
For IEEE, use of "et al." begins at three authors, and you use "et al.".
As you can see there are wild variations. Check which style you're supposed to use, and check how multiple authors should be cited with that style. As a general rule of thumb, maybe use "et al." when there are too many authors.
As another user pointed out it's also dependent on your field, and it's even possible that author names shouldn't be cited in every reference (just a numeric reference like [42]) -- I just checked a math journal at random and this was like that.
PS: If you're writing something in LaTeX and are using biblatex, I want to advertise the commands \textcite, \parencite and \footcite. They are able to automate most of this (for example with the APA style, they correctly detect which citation is the first).
For more than two authors, it's generally the norm to say something like "As Andria, et al. (2014) discuss, ..."
The question is not about citation, as with a works cited page, but whether or not it is appropriate to introduce all authors when first stating the title of the work. ie "In such and such article by author A, B, C, and D...." I believe the question is: Must all authors A-D be noted or is it acceptable with less? In this case I'd say yes it is just fine as is.
First one et al. [APDH14]\textcite{APDH14}will just take care of everything according to the file style.