You can follow the trace of Canal Saint Martin on this map. The starting (or ending) point is close to Place de la Bastille. I already talked about this part, the so called Port de l'Arsenal, in some previous posts (1, 2). After La Bastille the canal goes underground, more or less until it reaches a point near Place de la République (the dotted line).
This is where you will find the more romantic part of the canal (with trees, pedestrian bridges...). Further up, the canal becomes more industrial (or rather used to be) and finally it reaches a basin, Bassin de la Villette (of which I plan to talk tomorrow).
Napoleon (sorry, it's he again) decided in 1802 to have the canal built. One of the purposes was to bring (relatively) clean water to Paris, the other was of course to use the canal for transport of merchandise. The port handling took basically place in the extreme ends of the canal, Port de l'Arsenal and Bassin de la Villette. The canal was finished in 1825, has nine locks enabling to compensate for 25 meters (80 ft) of level difference.
Part of the canal was later during the 19th century covered, (of course) due to Haussmann and the wish to open for large avenues and boulevards. More or less a total loss of traffic brought again the idea in the 60's to cover also the rest of the canal. Fortunately this never happened.
Today you can have a boat ride or take a pleasant walk on the quays - and there are plenty of places for refreshment.
Along the canal you can find the - at least for Frenchmen - well-known "Hôtel du Nord" - still there - which, with the pedestrian bridge in front of it, is the place of some famous film scenes; "Hôtel du Nord", Marcel Camus, 1938. The film was however made with studio decoration. A scene from "Amélie Poulain" was shot on the spot.
You can find most of these pictures on my photo blog.