Granted this isn't going to last you forever and the build I'm sharing with you isn't meant to be utilized for long term. For long term use, the same method of building is used, but the materials you'll want to replace regular dirt and soil and all from your environment, whatever just happens to be there, with clay and sand.
What you will need.
First thing is first. Clear your specific area of choice of all rocks, sticks, twigs and grass. This is where that shovel comes in handy to get rid of that grass. You can use stone tools if you want to go primitive. Clear out an around at least 1/2 a foot larger than you need for the walls of the oven.
Now comes the hard work. Using your shovel (or primitive stone tools). Stand or sit in the middle and trace two circles into the soil one inside the other. This is your wall's marker. Several inches away from the line of the inner circle, dig up the soil and really loosen it up real good. You're going to dig in about 6 inches deep. Your oven should have at least a couple feet for it's radius so you should be fine digging 6 inches into the ground.
Now that you've done that with the soil dug out and loosened up, go to your body of water and grab some, you may likely need to make several trips for this just for water depending on the quality of your soil, what you're using for the oven (Dirt, clay). The consistency you want is thick mud that you can sculpt with.
So pour in your water, get down on your knees in that center hole you dug and really work that dirt and water together with your bare hands. If you accidentally add too much water, you can go to another location to remove the top layer of grass and dig and bring in dirt from the other location. You're going to need to do this anyway to finish the grill.
Now that you have a thick mud, now is the time to add your grass into it and mix it well once again all throughout the mud. This will help give the mud walls strength to stand on their own.
Once you have a nice thick mud, start building yourself layers of mud within those two traced rings in the dirt that you made earlier. This is why the mud needs to be thick, you are building walls. Just keep layering the mud until your mud wall is roughly a foot high from the ground.
If you need additional mud, you can mix the mud and grass outside of the grill for the next layers, just obtain additional dirt off site from where your current build is and bring enough dirt, grass and water to make more thick mud.
Now you need to semi-weather proof it. If it were to start raining the way it is, it's going to be destroyed. Grab yourself a bunch of dead, dry wood, twigs, sticks, etc.
Your firewood needs to be teepeed inside the grill, don't worry about trying to make the wood touch the walls, you don't need that damn much. You just need enough wood to fire the mud grill the first time to bake it, to drive away all the moisture. Start your fire accordingly inside the grill.
No, you do not need to fire the outside of the grill, the inside will be just fine, and you don't need a super large fire either. There is no need to try to bury the grill in a huge bonfire, you just need to build a small fire and have some patience, and keep that fire fed. You'll likely need to cook the oven for a couple hours but this is fine.
While the oven is baking, if you have the materials already to build your shelter, you can go ahead and start building your lean to, or setting up your tent, whatever you're using for shelter.
Shelter should be the first thing you've already set up prior to building the mud grill in a survival situation. Shelter yourself from the elements first, with enough space in your shelter to store dry wood. You can survive several days without food and water but you'll survive less without shelter, dry wood for fires to cook your food. And yes you want to cook, foraging for berries and shit won't give you enough calories, you're going to need to kill something. If that is something you can't do, the outdoors might not be for you until you can get used to killing, skinning and gutting an animal then getting right to cooking and eating.
Overall this largely depends on your survival situation. You may need to set traps first, then build your shelter but you always need clean water. Just ... don't be stupid and judge your situation according to your needs. I'm a fat guy, I can do without food far longer than someone who's slender, but the slender guy and I will both survive in the same amount of time without water with neither outlasting the other for much longer. Different environments also call for different needs to be met first.
When I'm camping, I'm already salivating before and during the gutting. It is something you get used to, but if you quit, you never will get used to it.
Ok, now that the shelter and survival tangent is over.
After your mud grill is completely baked, it should be sturdy and survive several storms, but it will wither away over time. If you used clay and sand and fired it, it'll last much longer. Months to years longer depending on how well it's built.
Now to cook in it, you start your fire and get to where you have lovely coals burning inside it. Those walls are funneling all that heat straight up.
So remember that one line higher up in this article? Needing a flat rock, skillet, grill grate, etc? There's several ways to do this. You can set the grill grate and the flat rock. I'll show you what I mean, video below 4:00 in, that kind of rock.
You could make a tripod with several long branches tied together at their top and build a system to hold the grill grate up allowing you to raise and lower it and all that jazz, no problem there, get creative if you really must, no skin of my back.
So long as you got those coals burning at the bottom, my preference is to take the meet and skewer it on a long stick and lay the stick or sticks over the coals to allow it to cook.
One special modification I do with my mud grill is I use a stick that's larger around than the stick I'm going to use to make several grooves parallel to each other to hold my grill sticks in place on the mud grills walls.
Is a mud grill essential? Not really. Is it nice to have instead of a regular fire pit? Yup. Safer too.
