The text of an author or editor field represents a list of names. The bibliography style determines the format in which the name is printed: whether the first name or last name appears first, if the full first name or just the first initial is used, etc. The bibliography file entry simply tells BibTeX what the name is.
You should type an author's complete name and let the bibliography style decide what to abbreviate. (But an author's complete name may be "Donald~E. Knuth" or even "J.~P.~Morgan"; you should type it the way the author would like it to appear, if that's known.)
Most names can be entered in the obvious way, either with or without a comma, as in the following examples.
"John Paul Jones" "Jones, John Paul" "Ludwig von Beethoven" "von Beethoven, Ludwig"
Some people have multiple last names - for example, Per Brinch Hansen's last name is Brinch~Hansen. His name should be typed with a comma:
"Brinch Hansen, Per"
To understand why, you must understand how BibTeX handles names (for what follows, a "name" corresponds to a person).
Each name consists of four parts: First, von, Last, and~Jr; each part consists of a (possibly empty) list of name-tokens. For example the First part of Per Brinch~Hansen's name has the single token "Per"; the Last part has two, "Brinch" and "Hansen"; and the von and Jr parts are empty. If you had typed
"Per Brinch Hansen"
instead, BibTeX would erroneously think "Brinch" were a First-part token, just as "Paul" is a First-part token in "John~Paul Jones".
Here's another example:
"Charles Louis Xavier Joseph de la Vallee Poussin"
This name has four tokens in the First part, two in the von, and two in the Last. Here BibTeX knows where one part ends and the other begins because the tokens in the von part begin with lower-case letters.
If you want BibTeX to consider something a single token, enclose it in braces. You should do this, for example, if a comma is part of a name:
"{Barnes and Noble, Inc.}" "{Barnes and} {Noble, Inc.}" "{Barnes} {and} {Noble,} {Inc.}"
The braces surrounding the comma keep "Inc." from being interpreted as a First token; this name has only a Last part, with either one, two, or four tokens (there must be a space separating the tokens in the second and third forms). Probably the second form is slightly more meaningful, but don't lose sleep over this since only rarely will an institution be an author or editor.
So the two names
"von Beethoven, Ludwig" "{von Beethoven}, Ludwig"
are considered by BibTeX to be different names. In the first, "Beethoven" is the Last part and "von" is the von part; in the second, which in this case happens to be incorrect, the Last part has a single token and there's no von part. The bibliography style will probably print both the same, but it may alphabetize and label them differently.
"Juniors" pose a special problem. Most people having "Jr." in their name precede it with a comma. Such a name should be entered as follows:
"Ford, Jr., Henry"
However, a few people do not use a comma. They are handled by considering the "Jr." to be part of the last Last token:
"{Steele Jr.}, Guy L." "Guy L. {Steele Jr.}"
This name has no Jr part.
To summarize, you may type a name in one of three forms:
"First von Last" "von Last, First" "von Last, Jr, First"
You may almost always use the first form; you shouldn't if either there's a Jr part or the Last part has multiple tokens but there's no von part.
If there are multiple authors or editors, their names must be separated by the word "and", surrounded by spaces, not enclosed in braces:
AUTHOR = "Ralph Alpher and Bethe, Hans and George Gamow"
Since BibTeX interprets commas as separating parts of a name and "and" as separating names themselves, this example has three coauthors: Ralph Alpher, Hans Bethe, and George Gamow. If the word "and" appears as part of a name, it must be enclosed in braces, as in the example of "Barnes and Noble,~Inc." given above. If you have too many names to list in a field, you can end the list with "and others"; the standard styles appropriately append an "et al."
BibTeX's rules are actually a bit more complicated than indicated here, but this description will suffice for most names.