SPOILER ALERT - DO NOT READ FURTHER IF YOU LIKE THE CHALLENGE OF FIGURING THINGS OUT FOR YOURSELF.
However, if your will isn't strong or you've just given up trying, scroll down...
AGAIN, THIS IS A MAJOR SPOILER ALERT. DO NOT SCROLL DOWN...
Trillium is in some asteroids, but not all. It is a rich source of sub atomic material used to power "faster than light" or "warp power" engines that can propel a space craft from one galaxy to another quickly. Your space craft has a "jump drive" which allows you to jump from one point in space to another quickly and beyond the limitations of Einstein's E=MC2 model. Lucky you, because no iPhone in the world has enough of a battery charge to stay on long enough to fly from one galaxy to another without a jump drive. And, it would be a bit boring.
The first level has the most and is the easiest level to find Trillium. Your Trillium storage tank will hold up to 25,000 pounds, which is well more than you need for one jump. We're not going to make it easy on you and tell you how much you need for each jump. Take some to a base for converting and you can do the math from there.
Each time you collect Trillium and visit a base, the base will convert this into "jump drive fuel". Your jump drive % indicator will show you how much of a jump you have (or multiple jumps). 50% means you don't have enough jump drive fuel. 200% means you have enough for 2 jumps. Pretty simple, huh?
We do NOT suggest jumping twice in a row and skipping a galaxy. Depending on which one you skip, you may have to go all the way through the galaxies again to get back to the one you skipped so you can complete that galaxies mission to complete the campaign. When you jump, you always go to the next galaxy. So, if you're in galaxy 2 and jump, you will end up in 3, etc.
To mine Trillium, find the asteroids with a green tint. It's hard to see them if you're looking "into the sun". So you have to plan your movement towards the asteroids to get the light behind you. Again, just like in real life. When you get close to a green asteroid, slow down completely. Your tractor beam will start to pulse. This is the magnet icon in the top left of the screen. It is pulling the Trillium out of the asteroid and into the Trillium storage on your space craft. If it's not working, you're not close enough, so get closer. If your tractor beam stops before all the Trillium is extracted, it's because asteroids lose mass as you pull Trillium out of them, and the asteroid has gone out of range. Pull up a little closer. The tractor beam is automatic and will turn on and off when you are in or out of range of the asteroid. Once all the green is gone, that asteroid is depleted and you need to find another. You will also hear the tractor beam while it is operating.
By the way, the same rules apply when you are retrieving a satellite or trying to "beam" a crew off a stranded spaceship... Hey, we told you this was a huge spoiler... Don't ever say Wings Galaxy is impossible to figure out... With the above info, you can now go through the campaign with complete ease... ;-)