Overall tempo is typically denoted at the beginning of a piece. It often gives you a clue as to the complete feel of a piece. The tempo can alter during the song, but the general feel is determined by the overall tempo. "Allegro" means lively or quick. "Andante" lets you know to keep your voice at a moderate pace. "Presto" requires you to sing quickly or fast, while "Lento" mean slow.
As a piece of music goes along, you might reach a part that requires an increase in speed. "Accelerando" means to accelerate the tempo. Often times the wording is accompanied by a line that shows you how much time you have to increase your speed. The amount of increase is decided by the conductor in order to keep the singing in line with the instruments. If you are singing alone, you have the option of setting the tone. For many smaller bands, the singer determines the pace.
There are a few words that mean to decrease the tempo. "Rallentando" means to progressively slow the pace. "Ritardando" is similar and means to decelerate. "Ritenuto" also works in a slowing manner but tends to resemble a more "held back" feel. This type of tempo adjustment is typically temporary and the pace will turn back to the former tempo. Ritenuto can be as short as a single note.
There are different types of rhythm for songs. Simple time allows for two or three beats per measure. Common time allows for four beats per measure. These beats are represented by notes and pauses to add up to equal amounts. Compound time changes beats per measure according to the current tempo of the music. This is another way to determine tempo when learning a new singing part. The length of the measures and notes tells you how quickly the song progresses through whole, half, quarter, eighth and sixteenth notes.