Leticia is just in the middle between Santa Rosa (Peru) and Tabatinga (Brasil). There are several ways to travel from Iquitos or Manaus to Leticia by plane, fast or slow boats. Immigration paper work is really important in this area but don't miss confuse just because we are an open boundary to fool with it or you will get a 400 USD fine. On each city (Tabatinga-Santa Rosa-Leticia) there is an immigration center so you can do your paper work right without any problem and remember that is free.
Remember that if you do an exit from a country (Peru-Colombia-Brasil), you only have 24 hr to do the entry stamp. If you stay longer without any entry stamp, you will get a 400 USD international fine. It's not a joke.