In the Roman mind, there was a sort of contract between the gods and the mortals. As part of this agreement each side would provide as well as receive services.

Thee role of the mortal in this partnership with the gods was to worship the mighty gods. For this there was prayer and sacrifice. And for both of these activities there was firmly defined rituals. To perform these ritual correctly was of paramount importance. One mistake and one would have to begin all over again.
The very nature of Roman religion itself, with its numerous gods, many of which had multiple roles, was cause for problems. Particularly as in some cases not even the sex of a deity was clear. Hence the phrase 'wether you be god or goddess' was a widespread in the worship of certain deities. Many Roman gods also had entire colelction of additional names, according to what aspect of life they were a patron to.
So, for example Juno was Juno Lucina in her role of goddess of childbirth. But as goddess of the mint she was known as Juno Moneta (this curious role came about because for a long time the Roman state mint was housed in her temple on the Capitoline hill).

There appear to have been few things for which there was not a special prayer. So, for example, there were prayers to bring bad luck upon another, or for the return of stolen property.

A prayer almost always will have been made together with a small offering to the deity. Such sacrifices did not always need to involve the killing of an animal, although this was very often the case. For the sacrifice had to be a symbol of life in some way or form. Milk, fruit, cheese, also wine were often used as less bloody offerings to the gods.
But naturally for the official rituals of the state gods it was animals which most of the time were sacrificed. And for each god there woudl be different animals. For Janus one sacrificed a ram. For Jupiter it was a heifer (a heifer is a young cow which has not yet had more than one calf). Ravanous Mars demanded a ox, a pig and a sheep, except for 15 October when it had to be the winning race horse of the day (the near side horse of a chariot team).

Such animal sacrifices were by their mere nature very elaborate and bloody affairs. The animal's head had wine and sacred bread (baked by the vestal virgins) sprinkled over it. The animal was killed by having its throat cut. But before it was sacrificed it was disemboweled for inspection of its innards, to ensure that the god was not offered an animal bearing a bad omen. Should indeed something be found wanting about the animal's entrails then it wa snot only a bad sign, but a new animal would have to be sacrificed in its place. For this there must obviously have been other animals standing by. The most important organs of the dead beast would then be burnt on the altar. The rest of the animal was then either moved away, or later eaten as part of a feast. A priest would then say prayers, or better he would whisper them. This too was a closely guarded ritual, by which the priest himself would be wearing some form of mask or blindfold to protect his eyes from seeing any evil and a flute would be played to drown out any evil sounds Should anything about the sacrifice go wrong, then it had to be repeated. But only after another, additional, sacrifice had been made to allay any anger of the god about the failure of the first one. For this purpose one would usually sacrifice a pig. Thereafter the real sacrifice would be repeated.

In order to avoid any embarassment from being caused with ill-omened bowels, or slip-ups in ritual, it was usual to make a major sacrifice on the day before a grand occasion. Like this any possible errors during the big event would be excused in advance.

The sacrifice of enitre multitudes of animals was quite frequent. It was no coincidence that there was a Greek word for the sacrifice of a hundred oxen - a hecatomb.

Roman religion did not as such really practice human sacrifice.
Although it was not totally unknown. in the third and teh second century BC it was the case that couples of slaves were walled up underground by demand of the Sibylline Books.
Also the gladiatorial games had their origin in sacrifices to the dead.