Pokemon Heartgold, How to catch Abra easily?

Since the only move it has is teleport, really the only thing you can do is just throw pokeballs at them until you finally get lucky. It will take some time, but it's basically the only way this early, unless you get something like a butterfree with sleep powder to sleep the abra, and then capture it.

The easiest way would be to catch a Pokemon that has a move that'll cause a status infliction before Abra can escape; the idea status infliction would be sleep. There's no easy way to catch an Abra (believe me) but if you can't get a Pokemon that can cause a status infliction, the only real way is to wait until you get a lucky break.

I always capture an Abra early on in the games, because of how powerful it becomes. I just chuck a great ball at it and hope to get lucky. It usually doesn't take long.

You get a fast ball from the old man after saving the slowpokes , use that. It should work better than a great ball.

Use great ball, that's all you can do.