Doomsday's strength is even more than that of Superman. He also has massive stamina, durability, speed, and agility.
He also has large bone-like spikes all over his body. These bones can be used as close-range weapons, and can even cut Superman. These bones also serve as armor for certain organs.
Doomsday can take massive damage and survive. When Doomsday is killed, he becomes immune or extremely resistant to whatever killed him. Every time he dies, he becomes more and more powerful.
Doomsday has an extremely strong healing factor. He is able to heal even after being turned into atoms, and scattered across the universe. While it will take longer to heal, depending on the wounds, he will still come back at some point.
Doomsday is able to sense, and probably track, Kryptonians.