Bleach: Undying features a fairly simple, lightweight system. Rather than being a full blown game system intended to resolve every possible action numerically, this system is more supplementary, aiming to give weight, structure and balance to action and character growth. To keep things simple this system really only has three major parts: skills, techniques and exp, which we'll explore here.
Skills
Shinigami rely primarily on four skills in combat, collectively called the zankensoki. For each of these skills your character has a score which denotes how proficient they are with it, each skill also has a physical characteristic associated with it, which is increased as your raise that skill. Each skill is graded on a possible scale of 1 to 100. As your progress through the rp you'll be able to raise your skill scores by spending experience points.
The four primary skills are:
Zanjutsu: Your characters skill with their zanpakuto as a physical weapon, it also raises your character's physical strength, as well as the durability, sharpness and so on of the zanpakuto itself.
Hakuda: Your character's skill with unarmed combat techniques. This skill also raises your character's physical endurance and toughness.
Hoho: Your character's skill with fast movement techniques suchs as shunpo. This skill also raises your character's physical speed and agility
Kido: Your character's skill with hado and bakudo spellcasting, as well as any kido based zanpakuto abilities. This skill also raises your character's reserves and ability to sense spiritual energy.
Techniques
Techniques are more specific applications of the four primary skills, they are particular moves which might be your trump card, signature or just a way to expand your combat capabilities, you can learn techniques from canon, as long as they aren't tied to something unique about a character such as their zanpakuto's unique abilities, but you can also create your very own techniques.
No particular technique is 100% necessary, as your basic skills will carry you pretty far in a lot of situations, but they can be a great way to further define your character's abilities. Just like with skills, techniques are graded on a scale of 1-100 and every technique is tied to a particular skill: to learn a technique your skill score must be at least as high as the technique's rank. New techniques are learned by spending experience points, you can also upgrade techniques you already know by investing more experience points in them later. To encourage experimentation with techniques, if your skill score is at least twice as high as the rank of the technique you want to learn than its cost in terms of exp will be halved.
Experience Points
Experience points are what you use to improve your skills and techniques and the work pretty much how you'd expect. You earn a certain amount of exp points for participating in story events and then you can spend those points however you like. It costs one exp point to raise a skill score by one point and learning new techniques costs exp points equal to the rank of the technique (though as mentioned above, this cost is halved if your skill score is at least double the rank of the technique you are trying to learn)
The majority of your experience points will probably come from story events, but you can also earn bonus epxerience by doing... pretty much anything really. Between missions you'll have some free time to write additional scenes for your character. You can explore their backstory, hang out with other player characters or npcs, explore and develop the setting and eventually take on side missions with combat. Any kind of optional scene like this will award bonus experience points to spend on your character, so the more you participate the stronger you'll get, but main story events will award enough exp that people who are less interested in this kind of thing or have less time to RP wont fall too far behind.
Everything Else?
If you know much about Bleach you probably still have some questions at this point. How do I unluck my shikai? or Bankai? Can I become a Vaizard? Or a Fullbringer? The answer is significant power jumps like the above examples are going to be unlocked through story events and they'll usually apply to the group as a whole, or at least the whole group will receive something equivalent even if they choose different things. I'm pretty open minded so if you have your eye on some particular goodie then I'll always consider how to get you what you want, but when you're able to unlock particular things will come down to the pacing of the story for the whole group.