The bobbin case comes out when the latch ( the part with the wick ) is removed on the early style, or the finger is lifted and rotated towards the sewer on the newer style.
But the oscillating hook does not come out unless you unbolt it from underneath. And when you do this you stand a reallly good chance (99.9%) of throwing it out of time.
The bobbin case will sometimes stick in place so oil and wiggling is the best course there.
Joe