Finding Demon Altars in Terraria

Solution 1:

Firstly you should try digging down in the corruption (or use bombs/dynamite) as there should be some alters underground there. However, if you are still unable to find any in the corruption then there will be some scattered throughout your world.

According to the wiki:

Altars encountered outside of the Corruption/Crimson on a given map will always be found at a depth of around 8 feet above.

So you should mine horizontally around this level if you intend to find some. As a reference, at a depth of 0 feet, the background changes from the sky to the cave background. So use this as a guide to finding 8 feet; if you haven't already found a depth meter or a GPS of course.

Solution 2:

Demon Altars spawn underground in the corruption (or very rarely thoughout the rest of the world), you won't see any on the surface. Keep checking chasms to see which one will actually lead underground.

If you don't want to explore and hope to find a deeper chasm then you can also dig your way underground. The easiest way would be to use dynamite/bombs to get through the ebonstone. I would recommend a grappling hook of sorts, so that you can climb back out to the surface. Or at the very least a mirror or recall potion to bring you back home.