The ideas behind the books
We have to face up to the fact that there is probably no such thing as time travel: it is not possible now, nor can it ever become possible in the future. We can prove that to ourselves simply by answering the question: 'where are they all, the time travellers?' If time travel were ever to become possible in the remote future, we would all, right now, be crowded out by people milling around in silver catsuits trying to mess about with the space-time continuum.
But it does happen all the time in books. It's an enticing fantasy - to be able to actually go back and live among people from past times to see what it was really like, and with the benefit of hindsight, to perhaps change a few things for the better. No matter what the fantasy, though, writers must create for us a world which stands up to a certain amount of scrutiny.
The major issue is to decide whether your characters can change the past. Obviously some small changes occur simply by travelling back in time. In 'An Angel for May' for instance Tam steals some clothes from a washing line in wartime England because his own clothes call too much attention to himself. Nothing significant stems from this so it is allowed to pass, although we only know with hindsight that this act of theft is insignificant. However, when Tam realises that his friends are in danger he tries to travel back in time for the sole purpose of warning them about the fire. The implications of allowing someone to live who might otherwise have died are too great though and Melvin Burgess backs away, so Tam doesn't work out how to pass through the portal until it is too late. Of course, if he had more control over the portal, with time travel there is no such thing as arriving too late. But I do like the way Melvin Burgess uses the time travel experience to change the present and future. When Tam finally returns to the present he understands why things are how they are and sets about changing them.
What you can permit your characters to do while they are time travellers obviously has a huge impact on the way you tell your story. In 'The Sterkarm Handshake' Susan Price wants to create a major interference with the path of history and achieves this simply by asking us not to worry about the implications:
Of course, she was a dimension removed from her own world, so this wasn't the 16th century of her own time-line - if she'd understood the scientific explanations at all correctly. But, she'd been assured, the two dimensions were so close, there was no essential difference.
So, once she's told us that anything is possible in this dimension, we go on to see settlers from the 21st century going to live 16th side, major 21st century surgery saving the lives of 16th siders and plenty of other dramatic events. It doesn't really matter what the rules are as long as they work for the book.
If time travel is in fact possible, it seems to me the only way it could work is for the traveller to find himself transported to a place where he can neither be seen by, nor interact in any way with the locals. He is merely a watcher. A witness to the facts. That may explain where all those silver catsuited people are - they're peering invisibly over your shoulder while you read these notes...