Alright, so here is how "Filler Days" Work. There are three phases to each day. Morning (which also melds into Noon as well), Afternoon, and Evening.
You get three Actions to do in the Morning. Three in the Afternoon. Then Two in the evening. This is for non school/work days. Mainly Saturday and Sunday. (As our characters do have school/work we have to worry about)
These are the 'Actions' you can do. Feel free to message anyone in the party to see if they will come help you out.
Fight a battle with some enemies to gain EXP, level skills, and obtain possible items (small fries will mainly drop small crafting items). Note that if you are in a party this is alot easier and faster. Grinding is done by rolling your attack and defense rolls (you telling me how you primarily want to attack and how you primarily want to defend and what Skills you are trying to level in the fight, up to 3). The enemies get their rolls (and bonuses depending upon how much they outnumber you by).
The better you do on your rolls than they do is how well you do in the battle (you will level your skills more and not get as hurt or tired, if you get a Critical then you get some additional bonuses). Note that you get up to three 'Grinding Chances'. If you do bad you lose one due to having to spend more time recuperating (unless you want to use Items to heal wounds and restore MP to bypass that). If you get a Fumble then you cannot grind any further and lose that action as you have to spend more time recuperating or use more items to heal yourself (if you are on your third chance and you fumble, then you lose half of your next action and can't do as much).
Note though when grinding you have the chance of encountering a Boss Mob (like the Big Imp from before). This fight will be played out and you CAN die during it, which is why I recommend being in a party of at least two if you decide to grind. If you decide to not fight the boss monster if you hide successfully for a while (this is a good use for Stealth) then the Boss Monster will eventually leave. You don't get any EXP or rare items from the monster that you would get if you killed it, but you won't die either. Note that when grinding at night you have a higher chance of running into some Boss Mobs.
[hider2=Skill Grinding]
Note that for Grinding you don't have to fight enemies either if you don't want to. You can instead just choose to grind a small set of skills outside of battle. This doesn't grant EXP from fighting enemies, but its a easier way to grind Skills safely without needing as much recuperation time (like using your combat skills on a tree or other such inanimate object or something, the Pseudospace prevents the tree from being affected in reality). This takes one action.
You can instead also do something like working out or studying. You have the chance of raising some of your stats and Talents this way. It takes all of the actions of the phase you are in and you must do it AT THE BEGINNING OF THE PHASE, but it is useful nonetheless to get stat and talent increases as well as a small bit of EXP.
You can decide to experiment instead. You can try to experiment with creating new skills or improving your current ones. Note though without proper 'Experimentation Skills' like basic martial arts techniques (like this Skill Rainer, an inactive character, had, see below*), Skills like Ren's Mana Focus, or other such skills that allow better experimentation then you will have a hard time doing so. Note that the Weapon Mastery Skills can make it easier to create special weapon techniques for instance.
[hider2=Basic Martial Arts Technique]
Basic Martial Arts Technique (MAX LV) (Passive): Fisticuffs +1. The basics of martial arts have been engraved within you through practice and hard effort. All Unarmed Strikes you perform deal more damage (1d8 instead of the base 1d6 (This cannot be seen in the skill window your character sees)). Through practice and diligence, you may be able to learn more powerful martial arts techniques as well.
You get three attempts per Experimentation Action. You tell me what you are trying to create/improve and how you want to go about doing so and I will make the appropriate roll(s) to see if you did create it. If you get a Critical then you will create something a little better. [/hider2]
There are numerous things you can do with Exploration. The first is exploring a district in hopes of finding something interesting (like Ability users) or getting to experience a cool event of some kind (you might even get a Quest of some kind) (what happens depends upon your Luck).
Next you can go shopping. You can either go to a common shop or explore around looking for a possible shop that would be willing to sell you special goods for Ability Users (although right now the chances of finding anything like that, or you all being able to afford anything) are low. You can also just go to stores to buy supplies (or to a sporting goods store to get some better basic weaponry) or even to a book store to maybe find some Skill Books (which you must buy before using). You can also try stealing like Sasha did (Val got REALLY lucky). I don't recommend it though as if you get caught a high chance of the Interference Law being invoked could happen (which means that you die) if they see you making stuff disappear.
The third is you can go visit any known NPCs that your character has encountered or knows about from the group (Right now you can visit either Saito Tatsumi (although you need to ask Ren or Lucian about where he can be found or just go look around yourself, they did meet him in the Business District) or Sumi Ban (you have to look up the address of the Ban family dojo first).
Exploration, regardless of what you do, consumes all of the actions in a phase of the day (unless its shopping. That only takes one IF You know where to go and shop for what you want. Otherwise it takes three if you are looking without knowing where to find it exactly or who to get it from exactly). Some special events can actually take the entirety of both the morning and afternoon.