- GM from a computer.
- Have a simple plot, with multiple explanations.
- Have maps, but don't use them.
- For the later campaign: Make history real.
GM from a computer:
As far as general advice, the most important thing is GM with a computer handy. Not just for note-taking, but so if the players surprise you, you can take a 5-minute break to google map and wikipedia-search the place they went to.
I kept a calendar for the game - it was a word processing document with a separate page for every day. I GMed with my laptop sitting next to me. Each page started with the date in big letters so I could find it quickly. I did my prep-work in it, color coding things. When the PCs left a scene by spanning away, I noted the day they spanned to. In that way, it became like a master span log for the whole campaign.
- Green meant "Planned, but not set in stone".
- Black meant "it happened, but wasn't viewed by a PC, so there's some wiggle room if things change it."
- Red meant "This happened in a scene, and is set in stone. Changing this creates Frag."
- Eventually, I had to add a fourth color for events that had happened very differently than what I'd planned, so I could highlight things that needed updating as they happened. I'd then actually update them at the end of the night, and didn't have to spend time typing up complicated explanations in the middle of a scene.
Have a simple plot, with multiple explanations:
In the early stages, you can be fairly plot-light. Throw one simple dilemma at the players, and let them deal with it. Being able to time travel and teleport is interesting enough to carry several sessions without much need for added complexity. I went overboard in the first half of my campaign, and I think it would have been better if I'd delayed half that plot by 5 or 6 sessions. Give them a small mystery, one that can be solved by clever use of time-travel, and they'll have fun doing so. They'll probably screw it up a couple times first, and have to unfrag themselves.
At the same time, drop in little hints of weirdness, of faux-complexity. Have a PC stumble across a weapon or tool behind a sofa, implying that someone has set up a slipshank and will need that tool in a future scene at the same location. Have a person in a fake-looking beard watch them from the corner cafe. This sort of stuff looks sinister, but is actually par-for-the-course for information-controlling time-travelers.
Players being players, they'll get paranoid, but this sort of thing is perfect. Once they get the swing of how time travel works, PCs will set this sort of stuff up for themselves all the time, and your "hints" then retroactively become mundane. Having it present before they get to that stage adds to verisimilitude, and heightens tension in the early campaign. With all these spanners in the mix, cause and effect don't necessarily have to be close to each other in time or space.
Time travel gives the GM an escape hatch. If some sinister clue turns out to be not what you wanted, just let the PCs go back and plant that tool behind the sofa themselves. Suggest that the guy in the fake beard might be an enemy, but he also might be your mentor (or elder self) checking in on you. Again, you don't have to really put out much plot at first, the players will generate it themselves just getting used to the ramifications of spanning. The nice thing is, you can put a bunch of strangeness out there in tiny doses, and then latter reverse-engineer whether it was hints of something big, or just their mentor acclimating them to post-level life.
Not that I'm advocating massive ret-cons and red-herrings. In general, I feel GMs should always know what's really happening in their game, and not change the shared past unless the situation is exceptional. However, Continuum is not like any other game you've ever run. It can be helpful to have two different explanations in mind for certain critical junctures, and hold off defining which explanation is right until after you see the player's reaction to it. You need to know when to reign in the confusion, and when to revel in it.
Have maps, but don't use them:
If you anticipate a fight scene or time combat, I recommend having detailed maps ready of the relevant areas. Don't show the maps to the players, though. Information control is everything, both in-character and out-. You want the maps handy on your computer, so when they hop off to ambush, you know what's there without pause or waver. But avoid minis (and showing the maps to players) like the plauge - you'll find that even if you love them in other games, in Continuum minis are a nightmare.
Time combat involves fragging actions - the same critical moments will get revisited again and again. While it's all just in our heads and the shared narration, minor inconsistencies are easily glossed over. But once you put mini to map, the players start thinking about line-of-sight, and want to rewind to 3 rounds ago when they had a better shot. You'll never quite get the minis positioned exactly right again, there'll be disagreements about who was where, and it won't be worth the headaches as it takes you out of character.
Make History Real:
When the campaign had advanced for a while, and the Players were ready to start exploring more of time, I found it very helpful to find just a couple of details to focus on in any era.
I picked up some cheap costuming and history books, and book marked them - when the players arrived at a new place or time, I could flip straight to images of the fashions of the era. I'd sometimes have photos of places prepared for when they arrived. I also researched what the food would be like for each era, as that was a great way of making things real (and sometimes disgusting). This was a lot of work, but it paid off really well, and made the second half of the campaign (the century-hopping) feel very different from the first half (which was all focused on a month-and-a-half in a single city).
Part of how I was able to do that without wasting research time was by having the NPC Mentor be several levels of Span ahead of the players. The PCs could go places, and hop around within a few years, but the NPC mentor was the person who took them to Ancient Rome, for example. She was happy to show them around, but they couldn't get home easily without her.
The ability to teleport and time-travel doesn't play as much havoc on the GM as you might imagine, either. The 4th Maxim dictates that players can't just hop around willy-nilly, they need to do so out of the eyes of the public. Oh sure, they may want to go visit Feudal Japan this session, but if they don't know a safe corner to span to, it ain't happening.
On the other hand, when the much-prophecied poop hits the proverbial fan, the untethered players can get pretty crazy. They'll time jump like crazy, with slipshank and other tricks making a complicated mess of the situation quickly. See my map-related advice, above.