Hit dice have something of a misleading name. It would be better to call them something along the lines of "hit point dice".
They serve two functions in the game. First, they determine your max HP. At L1 a PC gets the maximum roll of their hit dice (so like hte fighter's hit die is a d10, so they get 10), plus their con mod (we'll use +2 for our example here). This means that a L1 fighter starts with 12 HP. Each time they level up after that they get to roll their hit die (or take the high average), and add that plus their con mod to their max HP to get their new max HP. So back to our fighter example, when he goes from L1 to L2, he gets to roll his hit die, lets say he gets a 6, which is the high average), and then add his con mod. So a L2 fighter would have 20 HP.
The other thing that hit dice are used for is for healing during a short rest. If you take a short rest following combat, you can spend (roll) hit dice and add them to your current HP to take you up to you max HP.
So yes, you are currently using your hit dice wrong. The monster stat blocks are worded like that to show you how the monster's HP are arrived at (2d6's average is 7). If you want to randomize the HP for your monsters you can roll instead of taking the average (it's the same thing for monster damage, they give you the average, you can choose to randomize it with the dice expression provided).
If you were watching someone play the first adventure of the 5e starter set, most of the monsters there are goblins with 7 HP and, yeah, most L1 PCs can one shot goblins. This is normal.
This will unfortunately require a bit more work than you probably want to do when running the starter, but it's doable. You need a copy of this document. Take a gander at the second to last chapter and there you will find the encounter construction rules.
Basically what you need to do is find the encounter construction rules, reset the XP budgets to be for 6 players, and then rebuild each encounter with the appropriate number of monsters.
I would note that this is completely optional. You can run this straight up, let your party mow through it, and simply chalk it up as a learning experience.
One last suggestion if you don't want to change anything at all, is to adjust monster HP and damage. This is something I've experimented a bit with in my games with fewer people, but it's something that is definitely worth trying as monster HP and Damage are significant scale factors in 5e. Each monster has their average HP and damage listed. use a midpoint between their average and their high.
Best Answer
Flip back to pages 54 and 55 of the Starter Set's adventure booklet, at the beginning of Appendix B: Monsters. This section explains how to read the monster's stats. I want to bring your attention in particular to the text in the heading Actions (p. 55, bolded phrase my emphasis):
So "Hit 13 (2d8 + 4)" tells you what happens after you've already made a to-hit roll and it landed: an average of 13 damage, which is the average of 2d8 + 4 damage. You can either just deal 13 damage, or you can roll for it (but not both). The average is the same, so it's up to you. Since taking the average for damage isn't an option for players, no average is listed beside die expression for damage on character sheets and they always roll for it.
The "+X to hit" is what you add to the d20 roll to hit a target AC.
Putting this all together, you can interpret the notation on the character sheet too: "+4, 2d6 + 2 slashing" means that the attack roll gets +4 to hit, and (if it hits) does 2d6+2 slashing damage.