Consult the devwiki for a primer:
http://www.alientrap.org/devwiki/index.php?n=Nexuiz.Assault.
Currently, there are two objective types, trigger [activation of any triggering entity] & destroy.
Assault is CURRENTLY handled in time-limited rounds for which the opposing teams swap places as a round is ended by victory by the offence, or by round timelimit; the emphasis is placed on scoring frags, although it is likely to be replaced with UT Assault scoring.
Be aware that it is extremely difficult & requires drastically different design considerations to create a decent Assault map, for which the length that Assault City has been developed can testify [Started 07/08/03 YY/MM/DD].
For further reference, visit the UT map design wiki, or if you hold greater interest, do not hesitate to contact me, SavageX, or Ronan.