Start by building a siding (also called a passing lane). Choose a straight stretch of track, branch off from the main line, run a parallel track long enough to hold your longest train with a little extra room, then merge back in. After the rails are in place, open the Set direction tool and make each rail on the siding one-way, pointing in opposite directions. This turns the siding into a safe two-lane bypass, so neither train ever meets head-on.
Notice the forks at both ends have turned red. These are automatic no-stopping zones that keep trains from blocking in the intersections. If the siding is too short to fit an entire train, the game won't route trains onto it at all, so be generous with length.
With the siding ready, open the depot and build a second train on the same line. For very long routes or higher demand, repeat the process and add more sidings. Each extra passing lane lets you add another train while keeping traffic fluid and construction costs low.
Adding more stations is very similar. Build a new station (1) and connect it to the main line (2). Then build at least one siding between the newly constructed station and the main line connection (3), so that it's separated from it. Now you can build a new train that services this new station.