It has always seemed to me that the Mathematical Community gives a high importance to the act of properly citing an author (Do not write Erdos! It's Erdős. Cauchy must be read as in French, not as in English...).
Hence, I thought that it might be useful to ask your opinion about how to cite correctly a foreign and/or complicated author name in the references. It seems that Bibtex handles only standard English style names well, and requires many workarounds for foreign names (see here). So it is better not to count on it too much.
Feel free to point out any suggestion, or even the problems you have come across when citing authors.
I'll start a list:
✔ First, Middle, Last - Names. OK, I think there are no doubts, "John Horton Conway" should be cited as "J. H. Conway". Note the whitespaces after each period.
✔ Spanish names: See the very good answer of Leo Alonso.
✔ "Nobiliary" names (von, van der, etc.): See the answer of R. van Dobben de Bruyn.
Chinese names: Here I am often in trouble. I read that Chinese write their surname first and then their given name, but I think that in papers they are usually swapped. Also I heard that many Chinese have the same surname.
THE FREE LOOKUP ANSWERS
The user zeno pointed out that the tool MRLookUp http://www.ams.org/mrlookup is free an can be used to get the bibtex of any article tracked by the AMS.
Federico Poloni also suggested MRef http://www.ams.org/mref.
THE "LET'S JUST CLOSE" ANSWERS
Some users voted to close this question for different reasons. I answered this question thinking that how to cite an author correctly is often a problem for mathematicians, so address it on MO could have been useful for many users. I can agreed to close this question, probably choosing zeno answer as the best, BUT before I would like to see more comments and opinions, especially about Asian names.
1) Many answered: "just look on MathSciNet". Unfortunately, MathSciNet is not free for everyone, so I think this is a quite unsatisfactory method.
2) The question is not about the transliteration of names, you can assume that the author already have a name written in a reasonable set of characters extending the Latin. The question is about the abbreviation of names in references.