Natalie B. of How to Start a Revolution in 21 Days asked on G+:
"Who's run Traveller? Has anyone ever written about the procedures involved in running Traveller, a la what Sham's Grog n' Blog did for megadungeon play?
I have a pretty good handle on how to prep Traveller (I think) but a much less solid idea of what a typical Traveller session looks like, and what the engine of play is."
I think this is a great question, and while I gave her a very preliminary answer on G+, I thought I'd expand on it here. I'll be talking mainly about Mongoose Traveller, which is the version I'm most familiar with, and I'm going to stick to talking primarily about the corebook rather than all the supplements.
The core of Traveller is a resource management game, much like D&D. Money. time and opportunity are the player character's resources. The purpose of the ship mortgage and any other debt they acquire is to put a compelling time pressure on them and force them to prioritise, choose and pursue opportunities, which in turn get them the money they need to reset the timer. This is the core engine of play, and all the worldbuilding procedural stuff exists to flesh out these things in play.
To make this engine work, time needs to be tracked closely. Jumps take a week each, with a week of refueling between them in most cases. This means that in most cases, PCs have at most two weeks in a given system to make good on every opportunity available - less if they have to jump more than once or if they have to travel between the capital planet and the jump horizon. Depending on the referee, you may enforce that the PCs can only make payments on their ship in systems that have the complex credit arrangements necessary, meaning they have to spend time going back to these systems, intensifying the pressure on them.
Travelling itself imposes costs. There's fuel, crew costs, maintenance, and then any additional costs for dealing with danger, like buying weapons, repairing damage, etc. There's the costs of picking up trade goods if you're trading, there's port fees, there's taxes, etc. These costs should be concrete whenever possible. You want the PCs to see their bank accounts constantly ticking down, with occasional top-ups when they accomplish something. Usually, you want them to begrudge paying these, since it will drive further opportunities - smuggling; handovers in shifty, isolated locales far from local governments; taking occasionally foolish risks to squeeze out those last few credits or avoid handing them over to someone else.
The last piece is to generate more opportunities than the PCs can possibly ever accomplish, and then to make them either time-limited, or randomly occurring. This forces prioritisation. The most boring Traveller games are the ones where there's only one thing to be doing at any given moment. Opportunities should take different forms - mercenary tickets, booming markets, patrons with urgent requests, secret tip-offs and treasure maps, disasters, the locations of lost systems, illegal ancient alien technology, gold rushes, etc.
By altering variables of opportunities, the referee can influence PC behaviour quite strongly - if all roads lead to system X, then chances are the PCs are going to system X, whereas if everything goes in different, incompatible directions, the PCs are probably to pick either the safest or best paying option.
The last thing to bear in mind with this engine is determining how it faces the players. What information can they obtain before making decisions, and what's a gamble? How do PCs get this information? My experience personally is that the more information the better. The more factors the PCs have to account for, the more agonising any decision is. If you're going to leave a gap in their knowledge, then aim to either have it be to leave out a piece of information that will settle the decision either way for them, or that will drive them to want to acquire the answer.