This Is Fine - Playing touhou in expert summarized

1. A lot of the bullets are aimed at you and arround you. With some small, slow movements you can make the enemies shot at localized places, you'll see a lot of less clutter/chaos. This is called streaming. Personally i consider this to be the most important tip.
2. Conversely, a lot of the other danmaku patterns follow…patterns. You'll have to remain at the bottom, or in the center of the screen, or at the sides, etc. There isn't an universal guide, you'll need to see the patterns either yourself or in replays/videos. Also apply this to enemies (where they'll appear, which attack will they use)
3. The sprites (graphics) are bigger than the hitboxes (the area that is actually dangerous) (there are particular cases, like Sakuya's knives). This means that you can practically enter into a bullet (typicaly the bubbles) not dying. The danger is thanks to the overwhelming numbers.
4. Graze (getting close to a bullet without getting hit) is mostly for score, you can play it safe.
5. The main goal is completing the game, remember to use your bombs, spell card captures be damned, you'll lose your SC capture if you die, anyways.
6. Use all the screen. If you permanently remain at the bottom of the screen you can easily get cornered.

Just practice, remember to use practice mode and continues.