Just to clarify: my use of the word 'agency' in the above context was intended to connote the action, medium, or means by which something is accomplished, rather than a specific trading entity. That is not to say that crew members cannot also be recruited via an actual shipowners' agent trading as such.
I don't know how far you want to take this but anyone walking in off the street into a shipowner's Crew Department 'on spec' would need to produce previous certificates of discharge showing satisfactory performance in a given rating. If there was a slot for that rating, the candidate would be given a joining slip and told to report to the appropriate department head (Chief Officer, Chief Engineer or Chief Steward) on board the recruiting vessel with a view to "work-by and sail". The final decision then rested with the department head.
In case of candidates without previous seagoing experience there would have to be a specific need for that rating. If you were, say, a chef saucier and the ship's chef (big passenger ship) was still putting his kitchen brigade together, you might be in with a chance, given credible shoreside references.
If you were a 16-year-old from Muckle Flugga with a name like Murdo Maclachlan you might get a favourable hearing for a deck boy's job - these 'teuchters' had a reputation for being very handy about small boats and were excellent deck department material.
If on the other hand you were a hay heaver from Ashby de la Zouche you'd probably find yourself back out on the street again in short order!
In later years than Titanic one had to become a registered documented seafarer: the Dis.A was the key to employment. Also, for specified ratings, one had to be a member of the National Union of Seamen (successor to inter alia the two unions mentioned above). Even so, there were certain 'Listed' ratings (ranging from Writer to Flower Arranger!) which could by-pass those constraints, particularly with large passenger carrying companies. Otherwise, crew members were mostly recruited via the BOT Mercantile Marine offices rather than through shipowners' crew departments.