The Immigration Office is the best tool to micromanage your population level; edicts, pay and government freedoms will effect numbers on a wider scale.
If you set it to 'Open Door Immigration' and have average wages within $2 of the Caribbean Average you will see folks flood in, once your island is established. Set it to 'Love it or Leave It' and those who are least satisfied with your rule will set sail for pastures new.
It is awkward to tell if you have too many people, or are having problems with too few islanders. Good rule of thumb though, if you have almost all your job slots filled and perhaps 6-12 unemployed then you have a good pool of workers.(excluding educational benefits)
Finally, if you want to increase the number of people quickly, make sure you have plenty of job openings. Drop a few Log Camps or Teamter/Construction Offices and see them swarm in, so long as your pay is comparative to the Caribbean average and Immigration Office to 'Open Door'.