Elements of sacrifice include:
confession of sin
selecting a young, blemish-free animal (this involved personal financial sacrifice on the part of the agrarian Israelite making the sacrifice - he could have slaughtered the animal for food for his family, or sold it at market, or used it to work his farm)
laying hands on the head of the animal - symbolically transferring the person's sin to the animal, then putting that sin to death by slaughtering the animal
collecting the blood after slashing the animal's throat; pouring the blood around the base of the altar
collecting the fat and burning it on the altar
then the priests would eat the cooked meat of the slaughtered animal.
Necessary today:
confession of sin, then seeking God's forgiveness and aid to put to death that particular sin in the person's life
No longer necessary:
actual slaughter of an animal, or any of the rituals involved with the blood, fat, or meat. This is because Jesus was the ultimate sacrifice, and the only "blemish-free" sacrifice that could every truly be completely sufficient for God's righteous anger towards our sin.