Quite often its a fairly simple case of playing in a drum/rhythm track and recording a demo track onto it (guitar, singing, whatever you want to do) and messing around with the tempo until it sounds right.
Sometimes I'll step away from the DAW, imagine the piece in my head and then use tap-tempo into an app on my phone (Metronome Beats Pro on Android is a good app for this).
It's very easy to select one tempo throughout the song, and not vary it. However, the tempo of a song/tune may vary for effect as the piece is played. Craig Anderton did a good article on this some time ago (anyone have the link?) The choruses may speed up a few bpn, then slow for the verse, etc.