Janet's Thoughts on How to Dice

Use nA (claw) to get one into the air to cover an item throw, if you aren't actively being pressured - this can be looped for as long as they let you! Note that zoners can clear out individual airborne dice with projectiles, but the item setups and super meter gain can make this worthwhile. Letting you do this is a mistake from your opponent, but it's often safe to do this at least once without them having a chance to stop you! Also use nA to anti-air your opponent, if they're trying to very bravely jump in, hoping to catch you out.
Use fA (that punchy thing) to send one or two dice forward at great speed to punish a button or a backjump, or to juggle out of an anti-air. If you juggle, you should then roll to get closer, position your dice around them, and possibly juggle further.
Use jA (jumping attack) or bA (sweeping claw) to send one or multiple in a weird arc, slower than fA will - this is good for stopping the opponent from pressuring you, making space for you to do whatever you want, which is mostly toss out items because you're Lum. Also, the arc they fly in can be good for covering your jumps if you're going for some combo video stuff, apparently! Which is Lum's specialty, so it's worth knowing this, thanks MrMkl!
Use B (roll) to fire all of the dice at the opponent and deal chip (note that midori can escape this with dragon form's jB) - this is worse than most other options overall, but the threat of it keeps your opponent cautious (so do it every so often to prove it's a possibility!) and it works will for chipout situations (ie, when they're at 1HP). Note that this immediately removes the threat of dice while not giving you a chance to regain much super meter. This also gets you close to the opponent, which can be valuable!
Use jB to send all of them flying in different arcs (if one's gone offscreen slightly, this'll catch it and fire that one too) - this has very good coverage, and gives you an opportunity to toss out an item!
Use gS to show off and keep your jackpot safe from punishes.

Note that dice also "power up" your normals - you become safe from parries because the dice hit first, they can save you from cartwheeling into rook's gS (good ol' hitstun saving you from active frames, also you deal lots of damage), they mean that your nA into B does 3 damage and leaves you in a very strong position, they hugely power up your oki, and they give you psychological advantage in mixup situations because your opponent is scared!

Thanks to all of this, dice are absurdly powerful (they're quite probably one of the strongest things in the game), so having them out is ideal and often better value than jackpot! However, getting them out is usually higher risk than jackpot, and can be significantly negative value in some situations - they're more consistent, but jackpot has huge potential through fireworks and cakes, along with the chance to have powerful item setups for your current situation, so throwing out jackpots every so often even in circumstances where you could get out dice can potentially be of great value.

Setting up dice:

In general: Use items to force your opponent to stay out, removing any opportunities they might have to deal damage - the most effective items for this are bombs, thunderclouds, and minilums. Thunderclouds (and to a lesser extent minilums and bombs) stop them from approaching, and bombs also destroy level 1 projectiles, saving you from worrying about timing your jump. Note that to save you from a projectile, the bomb should detonate just before you land, not as you jump!
Versus Grave: Set them up while jumping over a fireball or bomb - beware his charged whirlwind during wind!
Versus Jaina: Set them up while jumping over a fireball or bomb, or when they go for rain of fire - dice win versus rain of fire!
Versus Geiger: Set them up while jumping over a bomb or minilum - anything such that Geiger can't use his gS (time stop) to anti-air you - or while Geiger has no super available. Make sure you won't land on a time spiral or poke!
Versus Argagarg: Set them up while jumping over one of their many projectiles. Make sure that they can't just fA (long forward arm) you as you land! Expect them to use their jS (big fish) when or after you do this if they can.
Versus Setsuki: Set them up while they're at fullscreen and don't have super and are busy doing something that won't let them B (ninjaport kick) to anti-air you. This won't come up very often, especially since you'll be using jackpot as a reversal lots!
Versus Valerie: Set them up after you knock them away and have some items between you. Generally you can expect to use jackpot too often to get many opportunities for this.
Versus Rook: Set them up while Rook's at fullscreen and there's items between you. This is very valuable, but you can expect them to often destroy at least one.
Versus Midori: Set them up at any point while Midori's at a distance, to make sure they're present during dragon form.
Versus Lum: Set them up while Lum's in the air - they're probably also throwing dice at this moment!
Versus Degrey: Set them up while a thundercloud's between you, or from next to a bomb and low to the ground - anything else and they can and should final arbiter you if they have super available!
Versus Quince: Set them up similarly to versus Degrey, as they threaten nearly the same things.
Versus Onimaru: Set them up at fullscreen while an item holds him back - anything else will let them B through the dice toss and destroy the dice (and maybe you)!

Each character's moves that can destroy grounded dice (note that dice can also be hit out of the air before they first land):

Grave: bA, jA, charged jB, gS, jS
Jaina: nA, jA, gC, gS
Geiger: bA, gC, low jC
Argagarg: fA, jA, jB, jC
Setsuki: bA, nA, fA, jA (any angle), gB (either), CA, jC, gS
Valerie: nA, fA, jA, gB, jB, gC, gS
Rook: bA, nA, gB, jC
Midori (human form): bA, fA, jA, gC
Midori (dragon form): bA, nA, fA, jA, gB
Lum: bA, nA, fA, jA, gB, jB, gS
Degrey: bA, fA, njA, jA, BA, BC
Quince: bA, fA, jA, gBB, jB, jS
Onimaru: bA, fA, jA, gBB, gC, jC, gS

Additional random stuff:

The distance from the dice when you hit them with nA will affect the speed and trajectory - the further back you stand, the faster and further forward the dice will fly. You can use this in conjunction with the ability to hit dice in midair with jA and jB to do… something. You can also hit a dice in midair with nA to redirect it towards the opponent, which is useful after propelling them upwards with nA to surprise the opponent (potentially after an item toss, and in the process potentially hitting another dice up), and can also catch dice that bounce back to push them forward.
Dice don't like to occupy the same space! If they do, they will push each other away and thus roll apart over time.

Other thoughts on stuff!