Time travel is a rich field in fiction. The lure of returning to past ages, and perhaps changing the outcome, is strong.
Time travel is devilishly hard to get right for RPGs, though. There are tons of ways you can set up time travel rules, and many of them can lead to disaster for the campaign (in the sense of nobody having any fun).
You can do a lot of research on possible time travel rules in movies and books, although much of what you find there will be inconsistent. Consistency is important, because your players will try to exploit the rules you create to the fullest. Being arbitrary, by allowing what you want to work and disallowing anything you don't want to work, is the surest way for everyone to have a miserable time. Coming up with a consistent set of rules and applying them fairly will help everyone have fun.
Here are some of the questions you need to ask yourself when designing your rules.
Can The Past Be Changed?
The chances are good that the answer to this is Yes if you're running a Time Police sort of campaign, otherwise there's no point. But if the answer is No, you can still have a lot of fun by allowing the characters and their adversaries to interact in past times. Temporal inertia will prevent significant changes, so some of what the time travelers try to do simply won't work...especially interesting if the two groups are bounty hunters and fugitives.
If the past cannot be changed, you'll need to determine how much change is allowed. Perhaps historically insignificant people can be diverted from their regular history, while the movers and shakers cannot. Or perhaps nothing can be changed, and any attempts at change will fail (the gun jams when you try to kill your own grandfather).
How Do Changes Move Futureward?
Most interesting is when the past can be changed. You'll have to determine how the changes move into the future.
One possible answer is "instantly". A change in the past will instantly reconfigure the future all the way to infinity. In this scenario, a temporal police HQ would need to be located in the distant past, to avoid being wiped out by changes in historical times.
A more typical answer is that changes move forward at a specific rate, giving a future temporal police force time to recognize that a change was underway and send back an operative. You don't actually need to specify the rate itself, that can be left to whatever is best for dramatic impact in any adventure.
Do Changes Move Pastward?
A change in the past affects the future, certainly. But can that change also follow a time traveler back into the past?
For example, let's say that Bob travels back in time to fix a high school prom disaster that scarred him for life. Bob is successful, and the change moves into the future, and the Bob of the future is a much happier man. But what about the Bob of the past?
Does he fade away, his work done? Does he now remember the changed past instead of (or in addition to) the original past? Does he remain the same, remembering only the disaster?
Did the Bob of the future come up with some reason to travel into the past, or are there now two of them?
Working out the answer to this question is one of the keys to figuring out what happens when your players start trying to work the time travel rules to their own advantage.
Are Time Travelers Immune To Changes In The Past?
Let's say that Alice travels back to the 1920s, and while she's there someone else makes a change in the 1800s that affects American culture in the 1920s. Does Alice remember the original culture, and realize that a change has been made? Does she remember only the new culture, herself having been affected by the change? Or does she remember both?
Making time travelers immune to changes in the past gives players some leeway for screwing up, but also makes it very hard to actually defeat the villain without capturing or killing him.
A better solution is often to make time travelers partially immune. They'll be affected by the change along with everyone else, but riding ahead of the change will be a series of precursor changes. Maybe history books and newspapers about the past change, while the present remains the same. The time travelers have a chance to see the changed history and get out of the present before the main change actually hits.
What Does "At The Same Time" Mean?
What does it mean to say that someone changes the past at the same time that Alice is in the 1920s?
Most time travel systems come up with the idea of meta-time, a sort of subjectively experienced time that controls when everything happens. Let's say that Alice and Bob both leave from the future at the same instant. Bob spends two weeks in the 1800s before making a change that affects Alice in the 1920s. Alice would have had two weeks in the original verson of the 1920s before Bob's change took effect (perhaps a bit longer if changes don't move instantly into the future).
Does Nature Allow Duplicates?
Can a time traveler meet herself?
Allowing this is the most interesting option, but be prepared for your players to try to exploit this to its fullest! Imagine a time traveler not only duplicating herself, but quadrupling, etc. A single time traveler could become a veritable army of duplicates. Of course, any injury to one of those duplicates would instantly affect any of the future duplicates.
To prevent duplication, assess severe penalties for it. Perhaps duplicates meeting explode, or one of them simply ceases to exist.
Don't Sweat The Details
You should think about the answers to all the questions posed above, but don't get a degree in temporal mechanics just to run a role playing game. When in doubt, use a movie or book at a model, and figure out their answers to the questions. When you run into a situation you're not sure how to handle, wing it.
You can always create some scientific gobbledygook for why the rules change later on if you mess up!