[D&D] How did I handle poison?

Party encountered an imp. I knew what imps look like and knew that they aren't that tough opponents, but when I described the imp and opened MM and checked it's stats I noticed that damn, it poisons.

In the middle of action I didn't have time to read about poison, so I figured it out myself. So, this is how it worked (gotta read it from rules though):

When imp hits it deals 1D4 damage + poison effect. I forgot to ask player to roll fortitude save, so she was autopoisoned. Every now and then when I see fit (few rounds or something) I ask player to make a fortitude save.
If she successes two fort-saves in a row, she is cured from the poison.
If she fails two fort-saves in a row, she gets 1 point of damage.

I have no clue how poison actually works, but I quess this imp was unique. I don't know if poison only affects predefined time or untill cured, or succesfull saving throw, but this imp was unique with his poison.

Oh, and the sting itches and burns. When another save roll is near, it always burns more.