In this video, an Aussie guy makes a natural draft furnace from only wild materials.
I happen to know a fair bit about survival and primitive skills and the like, so I'll just explain roughly what he does here, plus a bit on how to make the metallic iron into a tool.
So, the first thing to do is to dig a shallow hole, which can be done fairly well with just a blunt stick, to make the base of the furnace. Then make a circle of stones for the floor, ideally about 25 cm in diameter.
Now to get the material. For this, you could get clay from a riverbank, a termite mound, or (Since you mentioned that there was a bog nearby), turf. You'll need a lot of this.
Throw the clay into a large pit, pour a little water in and then mix it with a long stick. Then you'll need some kind of fibrous material (He uses palm leaves), which you should break into pieces and sprinkle over the churned, muddy clay.
Take the clay - which should be wet and gloopy - to your base, along with a vessel of water to moisten it if the need arises. Rub it onto the circle of rocks until it's smooth.
Now you can start to build the wall. Lay the clay around the 25cm circle of floor in a thick ring, leaving one section open. Keep on stacking clay on top of this ring, and after about 3 layers you can start to build over the open section too, forming a door-frame-like structure, but first lay rows of twigs underneath it so the clay doesn't fall in.
The clay will take a good while to dry, so you're probably only gonna end up doing a few layers a day. You should only add another lay after the ones below have hardened, and keep going until the furnace is about 175cm high.
Then what he does is makes something called a tuyere, which is an air pipe, out of clay. Stack a few layers of rings of clay to make a cylinder 7.5cm in diameter.
The next thing to do is to block the doorway, which you can do with more clay. However, make sure you leave a space to put your tuyere, which he puts into the doorway at a 15 degree angle downwards.
When you're happy that the doorway is sealed and the tuyere nose sticks into the inside of the furnace, you need to find your ore, break it into pieces, and roast it. To do this, make a type of cooking fire called a criss-cross fire. Basically, you light your fire, and then lay a lattice of logs (Leaving enough space for the air to flow through) on top.
Crush the ore to a powder and collect it in a container. Now, you need to make the furnace fire. You can use wood, but charcoal works best. I won't go into the details of making charcoal, but it's more or less lighting a fire under a big pile of wood and making a clay shell over it, then breaking it open the following day to find your charcoal.
Stack the charcoal all the way up to the top of the furnace, and then light it on fire at the top. The tall, narrow furnace creates a strong natural draft, and temperatures inside could get to 1,200 degrees centigrade, if not higher.
After an hour and a half of burning, the flames will eventually burn out. When you think it's cool enough to do so, take away the door-stopper and the tuyere and see if there's metallic iron at the bottom.
If there is, make a mold from clay in the shape of the tool you want to make. Melt the iron in a really, really hot and fire and carefully pour it into the mold, making sure not to burn yourself.
This is enough to give you one fairly good iron tool, but banging the metal with a hammer of wood or stone while it's hot will help shape it a bit more.
If these guys are experts in primitive skills, technology and survival, they could potentially do this, but it'd require tremendous expertise to carry out in practice.