Antedians were fish-like in appearance, but of similar size as many other humanoids and capable of bipedal motion. They ate fish like vermicula. Worf considered them to be "a handsome race," whereas Lwaxana Troi stated that the "last time [she] saw something like that it was being served on a plate." Their minds were highly susceptible to telepathic reading.
They were somewhat reclusive, and few Humans had seen an Antedian in the flesh.
Antedians found spaceflight extremely traumatic and survived the ordeal by entering a self-induced catatonic state. Upon arrival at the end of a voyage, Antedians required great quantities of food to replenish their bodies.
In 2365, the civilization was offered membership in the United Federation of Planets. The USS Enterprise-D escorted two Antedian dignitaries to a conference on planet Pacifica. Here, the Antedians were to be given a formal opportunity to join the Federation. However, immediately prior to transport down to Pacifica it was revealed, by Ambassador Troi, that they were in fact assassins and their robes were lined with ultritium. They had planned on blowing up the entire conference. They were detained on the Enterprise. (TNG: "Manhunt")
"an-TEE-DEE-an" was the pronunciation of this name from the script's pronunciation guide. 
According to an internal reference document, listing all the aliens seen in Star Trek: The Next Generation, which was circulated around the time of the production of TNG Season 5, the Antedians were given the description of "Fishlike in appearance with purplish-silver scales, half shut eyes."