I am just curious, do they make the decision before the conference?
Or do they watch the presentation of potential candidates first and then make the decision?
It depends.
Some conferences, such as ACM CHI, announce them before the conference even starts. This has the advantage/disadvantage of letting people know which talks they should see. And in my experience, these sessions are packed!
Other conferences announce them at the end of the conference. This has the advantage of keeping everyone at the conference until the very end (people might try to leave after their own presentation...) so they don't miss their own award!
It depends on the conference, though most of them in my experience make the decision after the talks.
Best paper awards are awarding the best paper, not the best presentation. They are common in archival conferences (i.e., conference that publish proceedings and that "count" as publications) like those that form the primary publication venues in computer science.
Because they are geared towards papers, they are almost always decided on well in advance of the conference. Often they are decided at the program committee meetings where the final decisions are made as to which papers will be accepted! When they are announced varies from conference to conference even within fields. Sometimes awards announced at the conference with a ceremony. Often, they are announced well in advance.
Conference that award papers earlier often do so that they can mark best papers on the conference program. In some conferences that list awarded papers in the program, best papers are not even formally announced. One year at Computer Supported Cooperative Work, I found out that one of my papers had received an award when I browsing the public program!
In most non-archival conferences (e.g., social science and humanities conferences) awards for papers are given for any work that was published in the field in the previous year. These papers nominated ahead of time and are not necessarily (or even often) work that is presented at the conference.
I've heard of best presentation awards given at the very end of conferences based on presentations given at the conference but I believe these are exceeding rare and, in my experience, have mostly been in the context of special conferences like doctoral colloquia.