With sheet music, tempo is designated either by metronome markings or various tempo terms. Metronome markings are numbers listed on sheet music that specify the tempo in beats per minute. The best way to achieve this tempo is to use a metronome. Set the metronome to the number listed on the sheet music. The metronome will then provide the appropriate tempo audibly.
Tempo terms are more open to interpretation than metronome markings. They give a conductor a guideline for how fast the piece should be played, but the exact tempo is set at the conductor's discretion.
If you are not using sheet music, then it is up to you to control the tempo. In bands, it is up to the drummer as to how fast the band plays. If your band is playing a cover song, listen to the original song to determine the approximate tempo. If you are re-interpreting the song, or playing an original song you wrote, the tempo is entirely up to you to specify. You might want to experiment with different tempos until you find the one that fits the song best.
Tempo terms written on sheet music are in Italian. They do not correlate to a specific number of beats per minute, but provide a basic guideline for the conductor to set the tempo. "Grave" means slow and sad-sounding; "Largo" means slow and big-sounding; "Larghetto" is slightly faster than "Largo"; and "Adagio" and "Lento" both mean slow. "Andante" is faster, and translates literally to "walking," which refers to a walking pace. "Moderato" represents a moderate or medium-paced tempo. "Allegro" means fast; "Allegretto" is slightly slower than "Allegro." "Vivo" (somtimes called "Vivace") means brisk; "Presto" means very fast; and "Prestissimo" is the fastest.
Many scores of music involve tempo changes. The same goes for many rock or jazz songs; the musical piece often changes tempos at some point. Tempo changes on sheet music are also designated with Italian terms. "Accelerando" means to gradually get faster, while "Ritardando" means to gradually slow down. The sheet music will designate when to begin speeding up or slowing down, as well as the point where the change should be complete. The term "Rubato" instructs conductors to be loose with the tempo, to allow the music to speed up or slow down occasionally, but not veer too far from the original tempo. Finally, "Tempo I" instructs the conductor to return to the original tempo.