This achievement is missable, but I've read a lot of guides and most people make it harder than it needs to be - sure, you need to make sure you light the fire, but you can wait until you've set the machine up entirely to do so! The goal is to make the smoke signals that match the symbols on the shaman's staff, but if you pay attention you can set everything up before lighting the fire at all.
First step is to grab everything you need from the bottom compartment of the device. You'll grab some resin (one whole blue chunk, one quarter red chunk) three funnels for the different shaped smoke, and a log. You can go ahead and put the log and the customs papers in the central burning chamber to get them out of your inventory, but don't light them yet!
Next, move to the side of the machine and turn the valve so it is vertical instead of horizontal.
Now to streamline things, exit out of the machine view and go to the log stump and cut the whole blue resin chunk into a quarter piece, and return to the machine view.
Now to set up the smoke stacks on the side of the machine closest to you. One by one, zoom in on the lower part of each smoke stack, and open up the compartment. If there is any resin in there already, grab it, and then move the upper "tray" up a bit and make sure the lower one has its handle facing out towards you so that when you lower the tray both handles are aligned. The idea is that it will force the smoke to go through the grill and be dyed by the resin you place on top and won't let the resin fall through. If you follow these instructions, the quarter of the tray you should place each resin block on will be the lower left (southwest, if that helps) section. From the left side of the machine to the right, you should put the resin quarters in this order: red, blue, blue, yellow. Before moving on to the next smokestack, be sure to close the resin section and turn the valve at the bottom so it is vertical.
Next step is to make sure you have the different funnels in the correct top section of the smokestacks (the section that bends away from you and is closer to the river) so that the smoke signals will take the correct shapes (again, you can take a look at Ayawaska's staff if you want to know what your end goal is). When you click on the upper sections, the camera will flip to show you the view from the other side. The third (when facing towards the river already has a funnel in it, but it's the wrong one. Go along the smokestacks and and open and place the funnels so funnel 1 goes into the rightmost chimney (from this back side, it's the leftmost on the other/front side, ie the RED smokestack), 2 in the one next to it, and then 3 and 4. Once you've placed the funnels and closed each stack, you can move back to the front view.
Last major step before lighting things up is to put sawdust in each of the four drawers below each smokestack. After you've done this and closed all the drawers you might want to take a moment to make sure all the smokestack "doors" are closed on both sides, and most importantly that all the valves (both the side one and the ones below each smokestack) are in the vertical position. As long as you've got one smoking you can tweak things once you've lit the fire if you made a mistake, but we don't want the smoke/fire to go out!
Lastly, light the papers and the logs underneath, and close the doors!