Alpha Muscae is the brightest star in this small constellation. It's found by dropping one binocular field due south from alpha Crucis: binoculars.

If you have a small telescope, beta Muscae (in the same field) is an interesting binary.

This is a close binary with orbit of 383 years. Presently (J2000) the companion is 1.3" away at a PA of 43º.

Also worthy of investigation is the globular cluster NGC 4833, quite bright and compact and just visible in binoculars. It's north-northwest of delta Muscae, in the same field of view.

A portion of the dark nebula known as the Coal Sack spills over into Musca, but most of it is found in Crux to the north.