Because he is a soldier, Captain America doesn't hesitate to kill the enemies. However this movie is set in World War II so this is expected.
A man is shot and you see a splurt of blood.
There are lengthy fight sequences featuring kicks and punches with sound effects of crunching bones as well as scenes of gunfire in which people are killed. But the movie is mostly without excessive bloodshed.
A lot of fisticuffs, gun fights and explosions in all of the action - far too many to detail here.