I have refereed the Lost Mine of Phandelver twice. The essential trick is to think of what you would be seeing if you were actually there and then roleplay that as the referee. Since you are presenting a situation that leads to adventure this will provide a natural way to hook into the information that the player need to proceed.
There two broad ways for the player characters to become involved. One is that their background has some elements that propel that character's roleplaying. If it result in a lead for an adventure then it often leads to the entire party going on that adventure. The other is that the players encounter something that provides a lead for an adventure.
In your case, there are a number of hooks in Phandalin that branch out to the rest of adventure. Now the background element in play is that they were hired by Gundren Rockseer to escort a bunch of supplies to Phandalin. They will be
ambushed by goblins outside of the village. From there they will get into Cragmaw Hideout and find Sildar Hallwinter and learned that Gundren Rockseer has been taken away to the goblin's main lair.
This should be the primary driver of the player's actions. The problem is where in the wide wilderness is
the Cragmaw's hideout?
For that they need to explore. They could aimlessly wander around but a smart player would know to start asking questions about the area from the locals.
The problem that could arise from this.
- The players lost sight of the fact their employer, Gundren Rockseer is missing.
- The players for whatever reason don't bother talking to anybody and thus not getting the clues they need.
Now I have ran campaign with what I call the really clueless party. Although I being a bit sarcastic, I always want my players to have fun. So I found ways to accommodate this and run an interesting campaign. Usually it is a result of the group being focused on killing things and taking their stuff. Which is fine, it just needs to be accounted for.
Specifically for Phandelver you have a way to deal with a clueless party.
It sounds like they have rescued Sildar Hallwinter. After transporting Sildar to the village he will be working with the Townmaster, Harbin Wester as part of trying to find out what happened to Iarno Allbek. For a clueless party, Sildar will come to the party with Harbin in tow. The two will offer the Orc Trouble quest and the Cragmaw Castle Quest. This is plausible because the party rescued Sildar, proving themselves to be competent.
the attack of the Redbrand Ruffian if this hasn't occurred.
You really need to piss off the players in-game with this encounter. The best way to do this is give them a scare combat wise. They will want vengeance. Also the villagers want
the Redbrand gone. So they will be actively telling the party where they are as the party shown that they are willing to stand up to the Redbrands.
There is a hook with
Carp the sone of Qelline Alderlead showing the party the secret entrance.
Do not give this to them unless it comes out naturally in the roleplaying. To keep things fun, there a minimum amount of information that is needed but beyond that the group has to earn it. If they get it
they will use the secret entrances into the Redbrand lair, if not they will use the upper entrance.
Once they deal with
the Redbrand, they will now know that Glasstaff has the backing of the Black Spider which establishes the primary villain. However they have no clue as to where he is.
Which is OK because they will have also rescued
Mirna Dendrar and her children. She will give them the tip about her heirloom and the Ruins of Thundertree.
Thundertree will lead them to the druid Reidoth, which lead them to Cragmaw Castle and the rescue of Gundren Rockseer, which will lead them finally to Wind Echo Cavern. They should want to ask Reidoth about Cragmaw Castle because of the reward promised by Sildar.
If you want to get them on the side adventures along the
Triboar Trail, then have the villager throw the group a heroes celebration after vanquishing the Redbrands.
Roleplay each villager with a hook in a natural way. Come off as everybody want the heroes to help them with something which will sound natural and unforced. In fact the player may wind up feeling overwhelmed.
But if you don't want to do that then the above with
Townmaster quests and Mirna's quest
is the minimum to propel the party to complete the adventure in a way that feels natural and not forced.