How is it determined if an Islamic man can have ...

Well to start with the simple things, it is illegal in most western countries to have more than one wife.  So, if it's illegal, then you can't regardless of what Islam has to say. 

Most majority Muslim countries (except Albania, Tunisia, Turkey, and former USSR republics) retain traditional Sharia which interpret the teachings of the Quran to permit polygyny up to four wives. Albania is a country where although about 70% of the population is historically Muslim, majority is non-confessional. Turkey and Tunisia are countries with absolute majority Muslim populations (99.8% and 98% respectively) that enforce secularist practices by law. In former USSR republics, prohibition of polygyny is the heritage of the Soviet Law. Currently there is a revival of polygyny in the Muslim World and there have been attempts to re-legalise and/or re-legitimise it in some countries and communities where it is illegal.

http://en.wikipedia.org/wiki/Polygyny

First the husband must obtain permission from his first wife to marry a second wife.  A man can have up to four wives.  He must be able to be fair and treat each wife equally and financialy provide for each wife equally.  Since this is difficult to do according the prohit Mohammed, saw, this is being practiced less and less, and becoming quite rare in Islam.