Where do I find alloys and elerium?

Alloy and Elerium are very common crafting materials, but I'm not sure how I acquire them.

How do I acquire more alloy and Elerium?

Solution 1:

In the early game, shooting down UFOs is going to be your only real source for these materials, so you're extremely limited to the amount of elerium and alloy you're able to acquire.

As you progress into the later game, the more advanced aliens, namely Heavy Floaters, Cyber Disks, and Sectopods, start to "drop" these items (or are built out of them).

In short, the only way to acquire these materials is to go on missions. Shooting down a UFO (or better yet, invading a landed UFO) is the surest way to get these rarities.