1. Setting.
Traveller was originally intended for groups to make up their own settings, so don't be put off by the size, scale, and sheer amount of material describing the Third Imperium. Ignore it completely to start off and nothing will be affected much, you can always introduce elements of it later. The origin of the Imperium was to have an "off board" major polity that could explain where people served in the army, navy, etc.. You can call it Empire, Imperium, Federation, Confederation and it won't make a bit of difference.
1.1 The Third Imperium of the 57th century (IY1105) is the default for a lot of people, you don't need to know the entire history, there are many summaries and introductions and elevator pitches for this setting - I'll post mine later on in this thread.
1.2 Also worth mentioning is your setting will grow with time, you will likely use what the players get up to and your own interests in sci fi to build the universe you and your players like to have adventures in.
2. Communicate with your players.
Traveller is a game for everyone to have fun. No one has fun if forced to play a character they don't like, in a game arc they don't like. If they decide they want to travel from planet to planet having adventures then forget about setting up a "crew of an ethically challenged merchant ship" - just give them a ship, or use the other methods Travellers have for getting from world to world. If they do want their own ship but don't want the minutiae of trading for upkeep then just grant them one - a detached duty scout, a lab ship, a noble's yacht, a pirate corsair...
2.1 talk about the sci-fi the players like, which books, TV series, movies, ask what sort of adventures they want to get involved in - exploration, investigating extinct alien races, interstellar war, colonising a new world, espionage...
2.2 Traveller has a lot of technology detailed at various TLs but don't feel beholden to it, if you want a scout ship equipped with a teleportation system to get to and from the planet then don't worry about what the TL chart says.
3. Have a session zero for character generation.
Get the players together to generate their characters, do it term by term, and encourage the players to think of reasons how their characters may have encountered each other during this prior history. You can encourage this with minor rewards such as banking a mustering out re-roll, or re-roll of a skill on a skill table, or allowing them to just pick that term's skills.
If time permits get them to roll a couple of characters, then let them pick which one they want to play initially. Keep the others safe though...
3.1 As has been mentioned downthread a session zero also gives you a chance to run a combat, run a sample problem solving exercise, show your players how the skill system works, social interaction with NPCs, this could be nothing more than a shopping trip, a simulation...
4. Have an introductory adventure in mind.
Mongoose offers many short introductory adventures that can get you started, or you can re-purpose an introductory adventure from a different game, or just make up your own.
4.1 I use Death Station as an introductory adventure for every group, other adventures do it just as well, I add the meeting with the PCs first patron, more on Eneri Kuvick and hos bodyguard Gurt later...
5. Listen to your players...
how is this different to communicate? Listen to them as they discuss things during the game, listen to them after the game. You are the referee, you can put them in situations that interest them, you can grant them clues and maguffins that further their interests and goals.
Always remember - this is a game, you play it to have fun, so have fun
Don't always tell the player what skill to use for a particular situation, let them decide the skill and characteristic they wish to bring to the task. You may disagree with their choice, but ask them to describe what their character is doing. This encourages role playing. The only caveat would be to insist the player chooses the most appropriate characteristic modifier, not just their highest every time
"1. I roll my engineering skill plus Int."
"2. I use my engineering skill to attempt to re-route the power distribution node, since I have to work out which way everything is flowing Int is more relevant than Edu in this case."
this may mean the player is making up technobabble - let them.
You may find some players don't like doing this, and prefer you to tell them, or they stick with example 1 type rolls. If that is how they want to play the game and they have fun doing it let them.
Try to keep all the PCs together, but if they do have to be doing different stuff make sure every player is involved, even if their character is not in the current situation. Every player should be regularly asked what their character is doing (I once ran RuneQuest with a table of around fourteen players - every one of them felt involved in the sessions). Even if the main group is involved in a critical situation, take a moment to ask players not in that situation what they are up to.
