The cheering expressions depend on the region and often even on the team. In Spain, for example, there is "Visca el Barça" for the FC Barcelona, or "Hala Madrid" for the Real Madrid.
In Mexico, the main teams have songs for being cheered.
You may say "Arriba el América", "Arriba las Chivas", "Arriba los Pumas", etc., as a way to say "go + team name"
During the game, fans normally shout instructions to the players ("¡Vamos!" -> let's go, "Órale", "Vas"-> Go, "Tira" -> Shoot), descriptions of what is happening ("¡Fuera de lugar!" -> offside, "¡Falta!" -> foul), wishes ("¡gol, gol, gol!" -> please let this be a goal), celebrations ("¡Gooool!" -> Goal), or insults to either players or the referee (I won't write any examples).