How to make drainage for succulents in old birdbath?

You'll have to, yess.

I would be very careful. There is a drill bit made to use on cement. Put masking tape on area before you drill. If it’s not too big it might work or it might break it. I sure don’t know what else you would do.

Kelli and MIke are right. There are cement drills that you can use and your bird bath should have drained holes. Be careful when drilling depending on how old and what type of cement the birdbath is will determine how well it can have holes drilled in it. Also be careful because the bit heats up and if you drill to fast you could crack your birdbath. After you drill the holes in the bottom lay screening in the bottom so that the water drains out but not your dirt. I would also put stone chips or pebbles in on top of the screening so that there is an extra layer of drainage.

Masonry bit that goes through concrete and drill with enough power. Drill a few drainage holes in the bottom and you're done!

The pebbles are a great idea. You can actually plant them right into the pebbles.

Succulents need very little soil to root into which makes them easy to plant just about anywhere. How about using soil in an old pizza pan or deep dish pizza pan? You could drill a couple holes in that and with some small peoples below it, it would be raised from the bottom of the bird bath so it can drain. You could then lift it right out and tip the bird bath to drain excess water. Be aware of the shallow roots when moving the pan around. Succulents are not as stable as other plants and can be uprooted with an accidental bump.