Elaborating slightly on David Richerby's answer: cite the paper with the authors in the same order that they appear in the original. Never reorder them for any reason.
The simplest reason for this is that people will expect that your citation matches the original author ordering. If the original paper has authors in the order A,B,C,D, and you cite it with authors B,D,C,A, a reader is going to think you are talking about a different paper by the same people, in which B was listed as the first author. They will probably figure it out eventually, but confusion will occur in the meantime.
For a deeper reason, there are two possible reasons why the authors wrote their names in the order A,B,C,D:
They made a decision that A should be considered the "first author", perhaps because A had the original idea or did most of the work.
They made a decision to list their names alphabetically, so that nobody would be "first author". This implies that they believe that all of them contributed (approximately) equally to the paper.
In either case, you should respect their decision. If you change the author ordering, it makes it seem like you are second-guessing their decision, as if you know better than the authors who did what on the paper. This will come across as arrogant and disrespectful.
You can't assume that the person who presented a paper at a conference is the one who did the most work on it. Maybe A did the most work but couldn't attend the conference for some reason. Maybe they all did the same amount of work, but B really wanted to give the talk and so they agreed to let him.
You also shouldn't assume that the professor of a workgroup is the one who deserves the most credit for a paper. In many cases, the most senior person on a paper is the one who is least involved in its details (because they are dividing their time between many different projects).
So if the paper lists the authors as A,B,C,D, cite it as ABCD. Some people think the use of et al is problematic, especially for alphabetically ordered papers, but if you must use it, cite as "A et al."