The axe is an essential tool in Grounded because you'll be needing to chop down grass, dry grass, and even clovers to create resources that you can use to create your base and a whole lot more. This is one of the first tools you will want to craft, because a lot of the early game requires you to have an axe to get through.
To make an axe in Grounded you will need to get Sprigs, Pebblets, and make some Woven Fiber. The Sprig and the Pebblets are found all over the place, but we will need to do a bit more to get the Woven Fiber we require.
First, keep an eye out for both Sprigs and Pebblets. Sprigs are small shoots of grass that haven't quite matured yet. They are light green with two leaves and once you get close enough to them they will be named and you can collect them.
Pebblets are small rocks you will find all over the ground. They are gray with blue spots on them and flash a white color that signifies that they are collectible.
While you're wandering around in the game, make sure to just collect Sprig and Pebblets whenever you can. You will need both of these for crafting various tools and base supplies throughout the game. So, there's no real reason not to pick them up because you can stack them pretty well.
Now comes the slightly difficult part! You will want to find Plant Fiber, which spawns on the ground. It comes in a couple of different looks, it's either a two leaved little plant that's barely out of the ground, or a spinier version that has a bunch of small prongs coming out of it. It's all over the ground, usually found near large grass growth.
Once you've gotten all the materials, you'll want to head over to the little Science Lab. This can be located right down the path from where you spawn.
Head to that machine with the arms and the centrifuge on the right. This is your Resource Analyzer, and it is crucial for finding new recipes to craft in the early stages of the game. Open that menu up and pick your Plant Fiber to be analyzed. Once you've analyzed it, you will now have the ability to craft Woven Fiber. You might as well analyze the Pebblets and the Sprig, so we get the crafting recipe for the axe.
The recipe requires you to have 3 Sprig, 2 Pebblet, and 1 Woven Fiber to make. Just hit the Craft option on the screen and you will have yourself an axe! This thing is very versatile, because you can use it to chop down various plants, but also use it as a weapon if you want.