Took me a bit to figure out, would be great if they have added a guide.
"Rough" gets you a Tier 1 + a extra Tier 1 item for each tier above 2
"Coarse" always gives you a Tier 2
"1:1" gives you a random item of the same Tier
"Fine" increases 2 tiers, but can't go higher than Tier 4
"Very Fine" increases 3 tiers to max Tier 5
Applying "Very Fine" to a Tier 5 will give you a tier 6 (ultra), this is the highest Tier of the game (as far as I know)
If you run out of energy, just feed the machine with a tier 1 item for +50% energy (all items give +50%, tier doesn't matter)
So basically you start with one material tier 3 and 50% energy
You put it into the machine on "Rough" mode and you get 2 items tier 1
Put them into the machine on "Fine" mode and you get 2 items tier 3
Into the machine on "Rough" again and you get 4 items tier 1
And so here's the game loop
You can also "Coarse" -> "Fine" -> "Rough" instead (get 3 items and only cost 10% more energy)
It seems the game is autosaved, you can go back to menu any time to check items discovered.
Researchers will tell you the exact description of the item they're looking for, its usually tier 3 or tier 4. When you give them an item with the exact description you get upgrades (faster energy regeneration, lower costs...)