1And the LORD called unto Moses, and spake unto him out of the tabernacle of the congregation, saying, 2Speak unto the children of Israel, and say unto them,
If any man of you bring an offering unto the LORD, ye shall bring your offering of the cattle, even of the herd, and of the flock. 3If his offering be a burnt sacrifice of the herd, let him offer a male without blemish: he shall offer it of his own voluntary will at the door of the tabernacle of the congregation before the LORD.
4And he shall put his hand upon the head of the burnt offering; and it shall be accepted for him to make atonement for him. 5And he shall kill the bullock before the LORD: and the priests, Aaron's sons, shall bring the blood, and sprinkle the blood round about upon the altar that is by the door of the tabernacle of the congregation.
6And he shall flay the burnt offering, and cut it into his pieces. 7And the sons of Aaron the priest shall put fire upon the altar, and lay the wood in order upon the fire: 8And the priests, Aaron's sons, shall lay the parts, the head, and the fat, in order upon the wood that is on the fire which is upon the altar: 9But his inwards and his legs shall he wash in water: and the priest shall burn all on the altar, to be a burnt sacrifice, an offering made by fire, of a sweet savour unto the LORD.
-- Leviticus 1:1-9 (KJV)
So, the one who brings an animal from the herd or flock as a burnt-offering must:
- bring the animal to the door of the tabernacle; then
- place his hand upon the head of the animal; then
- kill the animal. The priests collect the blood and take it to the altar, sprinkling it around and upon it; then
- flay the animal (פָּשַׁט, Strong's H6584 - pashat), i.e. strip/pull off its skin; then
- cut the animal into pieces. The priests take the pieces of the animal to the altar, then arrange them (lay in order) upon the wood which they have arranged (lay in order) on the fire of the altar.
In regard to the burning, the text says the priests "lay the wood in order upon the fire", and "lay the parts, the head, and the fat, in order upon the wood", so the method of burning was orderly and efficient (well thought out).
Since the altar had a square surface, 5 cubits x 5 cubits, i.e. approximately 7′ 3½″ (2.225 m) x 7′ 3½″ (2.225 m) in modern units, and the method of burning was orderly and efficient, then more than one sacrifice could be burned at any one time.
An animal brought as a burnt-offering from the herd or the flock had it's skin removed, and was cut into pieces. The priests then lay all pieces together (in order) on the wood upon the fire upon the altar, which burnt them to ashes.