The joining process was not widely known before 2367. Trill both joined and unjoined have served the Federation and in Starfleet since the 22nd century, such as Yanis Caed's previous host Ral Caed, though the earliest known Trill Starfleet Officer was Ensign Lera Kesta in 2161. (Star Trek: The Next Generation; Star Trek: Deep Space Nine, Star Trek: Intrepid)
Among joined Trill, reassociation with a previous host's lover is forbidden, and is punished by exile, which typically results in the death of the symbiont. Cassius Dao was in exile for past association when he arranged for the Dao symbiont to be illegally transfered to Jorian Zen. (DS9: "Rejoined", Star Trek: Hidden Frontier)
On average, only about 300 symbionts were available for the joining process each year. Prospective hosts are chosen by the Symbiosis Commission, and are usually put through rigorous testing to decide if they are capable of being Joined. Common belief among the Trill populace is that only one in 1,000 Trill are capable of being Joined, but the truth is that the number is closer to half the population. (DS9: "Equilibrium")
Unless the joined Trill objects, a prospective host can request a specific symbiont. Weaker hosts tend to be overwhelmed by the symbiont's personality, and hosts have different ways of coping with the memories of the previous hosts.
One of the most important parts of the process is the Zhin'tara ritual, where an unjoined Trill makes a connection between the current host and a friend or relative, temporarily placing the personality and memories of a previous host into the other. This is a way for hosts to gain closure, and is required by the Symbiosis Commission. (DS9: "Facets")