When you click on a midifile, the default player should load and begin to play the file. If it doesn't, you will have to load the player, manually. On the PC, you will probably find it under Start>Program Files>Accessories>Entertainment. Current versions of the players can be downloaded from the Microsoft or Apple websites. Then, you use the File menu to load the file, in the usual way. The player has simple transport controls, like a tape recorder.
An excellent site, with thousands of midifiles will be found at The Classical Archives, http://www.classicalarchives.com/link.html
This is well worth a visit, even if you aren't looking for classical midifiles because the site map page has lots of information to get you started on the midi scene. The FAQ answers such basic questions as, 'How do I listen to a midifile?' and 'How do I download a midi file?'
Just a few examples of the 'goodies' downloaded from the site:
Sousa: Marches; Bizet: Les Toreadors - great backing for percussion bands and all kinds of rhythm work (KS 1&2)
Faure:Sicilienne - accompaniment for Grade 5 flautists (KS 3&4)
Beethoven: Ode To Joy - backing to provide ensemble experience for beginner keyboard players (Not for teachers who are midi beginners, though, as it must be transposed and slowed down. But, this 'freebie' is much better than many commercially-produced files.)
This site also has biographies of the major composers and 'History Tours'. Music specialists will find materials here to illustrate most teaching points.