How do I deal with poison in Shipwrecked?

Poor wickerbottom got Shipwrecked. She cut down a tree and got bit by a green snake.

There's green bubbles at my healthmeter, and every so often the screen flashes green and I lose HP.

How do I cure myself of the poison?

To cure the effects of poison you need to consume Anti Venom:

Anti Venom is an item from Don't starve Shipwrecked. It is used to remove the Poison debuff. Crafting an Anti Venom requires 1 Venom Gland, 3 Seaweed, and 2 Coral. It is a single use item.

It is said that Snake Oil will, in due time when it gets a function, also cure poison.

Snake Oil is a very rare drop from normal Snakes and Poison Snakes.

It (currently) has no functionality or effect.

It is presumed to be an alternative to antivenom when it gets a function.

The other way to be cured of poison is simply to wait. Poison simply wears off after 3 days. Unfortunately, it gets worse before it wears off, starting at 1 damage every 10 seconds for the first day, increasing until it's doing 4 damage every 5 seconds for the last tenth of the third day.

The damage chart is in the wiki, but the practical upshot is that 3 days is 24 real-time minutes, and you'll take 48 damage the first day, 78 damage the second day, and 109 damage the third day. Either you use some Anti Venom, or you heal 235 damage over three days. I highly recommend Anti Venom (and/or wearing a Seashell Suit or Horned Helmet to prevent receiving Poison from physical damage in the first place), but if you can't find the ingredients, a reliable source of healing can work as a replacement.