[event 1],接着 + [event 2]
[event 1],[subject] + 接着 + [verb]
接着 + [verb]
接着 links two events with no gap between them: the second starts as the first ends. It goes at the start of the second clause or after its subject, and often has 就 or 又 nearby.
In a story, 接着 on its own, followed by a comma, moves to the next event: "next".
Before a verb, with no other event in between, 接着 means "go on doing" something that was interrupted.
然后 only orders events: this, then that, with any gap. 接着 says the second follows immediately or continues the first.
继续 also means "continue", and it can take a noun. 接着 needs a verb after it.