Hilchos Maasei Hakarbanos 7:7

Squeezing out the blood of a bird sin offering is a necessary component of the service, as all the altar gets from this offering is the blood. The rest of the offering (i.e., the meat) is eaten by male kohanim, just like the meat of animal sin offerings.

Hilchos Maasei Hakarbanos 7:8

When performing melikah, the kohein holds a bird sin offering with its feet between two fingers and its wings between two other fingers. He stretches its neck for a width of two fingerbreadths and nips the head. This was one of the most difficult parts of the Temple service. If the kohein held the bird in some other way, it remains valid.