I'm absolutely new to Pathfinder and table-top RPGs, and I don't understand how are hit dice used after leveling. AFAIK, hit dice are used to calculate yout max HP when you start playing, but how do you use them when you get more of them?
[RPG] How do hit-dice work in Pathfinder
pathfinder-1e
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This depends on a number of things. Do your players like to favor combat over other forms of role-playing? How long are your sessions? Do your players understand the rules well enough to where things are going to move by quickly (sounds like no, in this case)? Do you as a DM mind running a lot/a little/no combat in any given session? This sort of thing is highly customizable depending on your needs, and is thus unfortunately somewhat unanswerable.
Anyways, my personal recommendation would be to run a quick module or two before your main campaign. This will allow you to understand the sort of preparation a DM typically has for an encounter, as well as learning a couple of tricks here and there with DMing before you start your own campaign, which, in the long run, will be for the good of your story!
More importantly, it allows you to assess your player's desire for and prowess in combat. If it turns out they only make it through one encounter, then want to roleplay or ask questions or drink beer and relax for the rest of the session, you haven't wasted hours of preparation. But if they turn out to be some kind of death dealing blood-for-the-blood-god-skulls-for-the-skull-throne party, you are unlikely to run out of encounters! You don't even have to finish the module, really. Once you are confident in your ability to prepare adequately for your players, you're all good to go. Happy DMing!
I've also looked at the Pathfinder Roleplaying Game: Beginner Box GM Kit but I can't tell if that's a complete adventure, or just tools for creating my own.
This contains a similar one-shot adventure that you can use, but mostly contains more gear/creatures that are compatible with the Beginner Box rules. It also contains 2 pages of details/advice for using prewritten adventures.
Further, I've found Pathfinder Roleplaying Game: Beginner Box Transitions, but I don't understand how I'm supposed to use it. Are the characters we created "throw away?" Will this be enough for us to keep going? Where do we go next?
The Beginner Box Transitions are to guide you from using the Beginner Box rules to using the full rule set (more detail on how to cast, attacks of opportunity etc.). Your beginner box characters are not throwaway, especially not if you and the group have grown into them, if you want to carry on with them and want to use the full rules, do you best to convert the characters from the beginner box character sheet to the full character sheet
I have ideas for campaigns, but I still feel too inexperienced for that.
Look at the structure of the Black Fang adventure, it's a mixture of combat, puzzle, RP encounters on a map with flavour text written for each area and scant dialogue for NPCs. It doesn't have a fully realised world or detailed plot.
You can build adventures without having to write an awful lot.
The analogy of a television series is very strong (campaign = series, adventure = episode, encounter = scene). You can think of your campaign ideas as potential story arcs; because as you play the group won't necessarily follow the stories in your head and each adventure, they will have their own ideas and all of that will feed into a collaborative story that you can continue to build on and change as you go.
If you listen to the Penny Arcade Dungeons and Dragons podcasts, it starts off without much to any of the characters, over the course of several adventures, Chris Perkins eventually writes adventures based around each of the characters. No-one could expect him to write an entire adventure about the characters, without first playing with them and learning about the characters, the players, what they like and how they play.
When it comes to creating adventures be as brave as you like, the GM book from the the Beginner box has a pre-drawn map and details of how to build encounters. There's plenty of formulas to build a balanced combat encounter, and you can uses your ideas to build story encounters.
I am still a relatively new GM and only halfway through playing my first home made adventure (using the map from the Beginner Box GM Guide), the group I play with are really keen, are all learning as well. More than anything they're grateful that I'm putting in the effort to try new things and write an adventure for them. As all of your group are thinking "what next?" they should be happy to try new things with you and hopefully should have plenty of patience with you learning as you go.
Sergut's suggestion of using prewritten adventures is good, this will give you a chance to continue playing without having to build adventures and get confidence and experience of what the group enjoys so you can tailor your homemade adventures to the group. When it comes to your homemades, don't be afraid that you'll make mistakes; you'll all be too busy playing and having fun to notice.
Best Answer
Hit Dice determine the number of Hit Points of a character or a monster.
They are also used as an equivalent of Character Level in some case, for instance for spells that works differently depending of the power of the target.
For instance, the Adaro has 4d10+8 HP, i.e. 4 Hit Dices. If it is hit by a Color Spray (and fail the Will Save), it will only be blinded and stunned for 1d4 rounds, then stunned for 1 round. It would be the same for a level 4 Player Character.
Hit Points calculation for Player Characters
When your character starts, their Hit Points are the maximum of the hit dice of their class, plus their \$CON\$ bonus (minimum 1 after the \$CON\$ bonus, which is negative if the \$CON\$ is less than 10).
Each time they level up, they gain more Hit Points. To determine how much, this time you roll the dice of the class they take for this level and add the \$CON\$ bonus (minimum 1 after the \$CON\$ bonus).
Example: A Fighter with a \$CON\$ of 14 has the maximum of the Hit Dice of the class \$(\text{d}10) + CON\$ Bonus at the first level, so 10 + 2 = 12 HP.
He then takes another level in Fighter, and gains \$\text{d}10 + CON\$. Let's say he rolls 8. He gains 8 + 2 = 10 HP, for a total of 22 HP
For his third level, he decides to take a level as a Wizard (for the sake of demonstration :) ). This class' Hit Dice is a d6, so he gains \$\text{d}6 + CON\$. Let's say he rolls 2. He gains 2 + 2 = 4 HP, for a total of 26 HP
You also have to take into account the Favored Class Bonus, which can be either +1HP or +1 skill rank (or one of the racial variants, like those ones for the half-elves).
There are also alternative rules to rolling the hit dice, like taking half of the dice (rounded up or down), so a Barbarian player (Hit Dice d12) wouldn't be really annoyed because they rolled less than 3, four levels in a row.
I personally prefer “half the dice (keeping the 0.5*), rounded down if not integer” (so, for a Fighter (d10), the progression would be 10 at the first level, then (10 + 5.5 = 15.5, rounded down) -> 15 at the second level, then (15.5 + 5.5 = 21) -> 21 at the third level, and so on.
*: Since the possible values of a d10 are \$\left[1,2,3,4,5,6,7,8,9,10\right]\$, its "average" (Expected Value) is 5.5, not 5. The same goes for all "even" dices.