Once again congratulations are in order to you, the DM! Session 0 came and went, and you didn’t bail and the players showed up on time, mostly (you know who you are).
Now it’s time to introduce the hub for the Campaign, in this case: Phandalin! Have a town print out or two for the party, tell them about locations in town, the Inn, the Shop, the Temple, give them brief descriptions on the NPCs that run said locations, but it is best to introduce them via RP. For a short adventure, only keep 6 NPCs of function (Innkeeper, Shopkeeper, Misc Service, Positive NPC, Neutral NPC, Antagonistic NPC) with retinue being added as necessary. The trope of “Adventurers in an Inn” works great! Having a sociable Innkeeper who is impressed by the adventurers makes the Players feel like their characters are relevant and gives them incentive to interact and even posture in front of the other PCs. Spend 1-2 hours here, chatting, getting the Players used to their characters and each other.
WHAM!! The door flies open and an NPC rushes in, injured or panicked and brings disturbing news! Something bad happened! Thank the Gods there are adventurers in town to deal with the problem! In LMoP I have Sildar’s horse galloping down the main street and collapse in front of the inn. Worried Villagers recognize the horse and mention how Sildar Hallwinter had gone north to investigate the attacks on the caravans that had been happening recently, and ‘GASP!’ there are goblin arrows in the rump of the horse! Sildar must be in danger, please oh brave and trustworthy adventurers, rescue him!
At this point introduce the theme of the Big Bad Guy: goblins, zombies, demons, devils, weird creepy crawlies from the forest, pick your poison! As the Party travels from Hub to Location A (In this case, the Cragmaw Hideout), the journey should be an auto success, but the rolls should give you a narrative. Have 3 skill checks made by the party, each Character allowed to participate in one roll each. 1-9 poor success, 10-15 success, 16+ great success! They encounter these creatures for the first time on their way to Location A, this does not even need to be a proper combat, have the players easily overpower the 1-3 creatures and discover their enemies for the first time!
Arriving at Location A, let your players experience probing a dungeon for the first time! It’s dark, sounds distort in strange ways, voices and hints of the enemies ahead should give your party moments pause before they venture in. Be aware of the combat capabilities of your party, have the encounters start small, but feel free to have 1-3 enemies join the initial encounter if the party seems to be mowing through the enemies too fast. Your goal is a to have a medium encounter of 3-4 turns with enough enemies that the party feels in danger, but don’t drain all their resources, as you should be introducing the first powered up enemy of the theme. In case of LMoP, several goblins and wolves are being led by a Bugbear! Consider having two distinct camps within the dungeon, that would allow RP players to make the encounters easier by having the 2 camps turn on each other. In LMoP, Yeemik the Goblin dreams of overthrowing Klarg the Bugbear, this should not be forced and if the players enter the Hideout guns blazing then have the goblins come at them with no restraint. After the party has dispatched the goblins (or if the fight is happening right in front of Klarg’s cave) have a Sargent of the theme make their entrance. After a relatively difficult fight, the players succeed and find the NPC to rescue and make their way back to the Hub.
The players should arrive with a bit of fan fare and celebrations, rounds of drinks bought for them at the Inn, let them soak in victory and end the session with the players excited to interact in the Hub again.