Zerg player here. To give some context, I usually build spawning pool at 14 drones, then expand, and get ling speed asap.
If I scout a Terran building an expansion at the natural, I pump lings and try force a cancel. If forcing a cancel fails, I'll grab a fast third.
If I spot him building an expansion in his main (with an overlord) I will drone for a little bit, and have a pack of lings waiting in his natural for when he tries to fly the expo there. I'll start a baneling nest and stream small packs of lings to the natural, so I can deny this expansion for as long as possible.
If I am able to deny the expo for more than a few minutes, I'll either get swarm hosts, roaches, or mutas into the mix and push the main.