(My area of "expertise" is Roman Britain and Roman general history, but I think I can answer this question)

In ancient Rome, the collection of taxes was done by the publicani, public contractors, and operated in a tax farming environment.  Later, a direct taxation method would be employed.

The rights to collect taxes in a region would be auctioned off and the highest bidder won the rights to collect.  The publicani would pay the taxes to Rome and then collect, with interest, from the people to recuperate their loss.

The taxes were levied against all property, real estate, and slaves.  During the annual census each citizen's tax obligation would be determined by the censors and this information was used by the publicani to determine how much was owed by each person.  It seems that the tax rate was usually around 1% though it could fluctuate.

In the provinces, where it could be difficult to obtain accurate census information, the tax obligation was estimated for an entire region and then divided out by the number of citizens and collected.

This method of tax farming was, as you can imagine, very susceptible to abuse and corruption.  Augustus put an end to this practice early in his reign due to constant complaints from the people (particular provincials). In it's place a direct wealth tax and flat poll tax, were developed.  With this method, each citizen knew exactly how much they were required to pay; under the farming system your taxes were whatever the publicani thought they could get out of you.

It should be noted that the term publican does not actually mean tax collector, they were just general governmental contractors of equestrian status.

Sources:

http://www.unrv.com/economy/roman-taxes.php

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Vectigalia.html

Edit: added disclaimer to the top regarding my ability to answer competently

How would they go about collecting the direct wealth tax?