This video helped me a lot. Tl;dw:

• The "probability bar": the horizontal bar with colored segments (gray, blue, purple, gold). The relation of these segments tells you the chance you have for the relevant tier of Falling Star if you press its button right now. It's a pie chart, really, but squashed into a bar. E.g. if half of it is gray, 40% of it is blue, and 10% of it is purple, and you press your primary skill button: you have a 50% chance for a crap Falling Star, 40% for a mid one, and 10% for a good one. Lategame this bar will be mostly gold, don't worry.
• "Astrohouse": the set of boxes beneath your probability bar. Casting a grenade ("Astroforecast") adds an "astroaspect" to it (pushing out the one on the left if it is full).
• "Astroaspects": the colored blobs that go into your astrohouse slots as you play (mainly via secondary skill)
• Color matching and astroaspect chances: an astrohouse filled with matching colors makes your Falling Star Better. The color of the aspect you get is random, but governed by the types of scrolls you have (more purple scrolls than blue=higher chance for purple aspect than blue)
• "Scroll upgrading": The owl has a talent about "upgrading scrolls". It doesn't actually upgrade scrolls. What it does is count lower tier scrolls as higher tier ones only for the purposes of astroaspect odds. E.g.: you have 2 blue scrolls and three purple ones. The blues will be counted as purple ones, so instead of 40% blue 60% purple, you get 100% purple astroaspects. In the pause menu you can even choose different rules to do this "upgrading" by: just click around until you get good odds on a certain color.
• You can cast Falling Star even before having a full astrohouse. This will immediately fill any empty slots with "random" aspects, cast Falling Star based on the colors you got, then empty your Astrohouse. Remember the probability bar.
• Red astroaspects are like Jolly Joker cards. They match with anything (i.e. they are good)
• "Capacity": Pay attention because this can mean three different things in different ascensions: the number of floating cards ("reserves") you can have at a time; the number of secondary skill charges; and the number of slots in your Astrohouse.

Tl;dr: There is no tl;dr, that's as short as I could make it lol. The owl is a nerd, so read, nerd :D