The Gear itself is about as pseudo-science as a Gundam, but that doesn't mean it's not entirely implausible in it's actual design and workings... I've made a little diagram to try and assist, although what everyone calls each individual part may differ by preference, as an example I called them "trigger, handle, lever, and slide" above as well as in my Forest Gear Test Post and yet labeled them differently after talking to my roommate about what he would call each piece.
For starters the simplest controls of the gear are actually pretty easy to grasp and rather solidly established if you have a good eye for detail, those controls being:
1. Firing a Hook
2. Reeling in a Hook/Wire
3. Releasing an Anchored Hook
4. Use of an Anchored Hook as a Static Line
Obviously we'll start with the first of those four, Firing a Hook.
The firing of a hook is the most base knowledge required to use the Gear and easiest of the actions to figure out by watching the anime. It is accomplished by simply pulling the first (The higher) of the two triggers contained within the trigger guards. As an example here is Jean during Trost trying to fire his right and left hooks by pulling the first trigger and not being able to due to his gear being broken.
As is easily seen he is pressing the first of the two triggers in order to fire a hook. Simple enough. Onto the second action.
Reeling in of a Hook is another rather simply accomplished action. It consists of holding down the first trigger after the hook has anchored itself in a surface and causes gas to be blown through the fan section on the specific side of the user which causes the wire to be reeled into the body of the device. A great example is Eren vs the Colossal Titan during it's short appearance in Trost.
He is stationary although having a hook anchored in the nape of the Colossal Titan, but once he pulls the first trigger on the same side that he has already fired and anchored a hook, the wire begins to be reeled in. Since he hasn't released the anchor this action instead brings the user
to the anchor and not the other way around. (This is how you pull yourself forward without the use of gas).
The Third action is the release of an anchored hook. This is done by pulling the second (lower) of the two anchors. I couldn't find a good example of this taking place, but due to the fact that the first trigger has a very defined set of actions it performs and the other mechanisms don't seem to release anchors it leaves it as the only real option left. Pulling the Second Trigger is assumed to break the hook free of its anchor point by extending the side of the anchor toward the front and essentially breaking it free or pushing it off of the surface it is in.
The Fourth action is using the wire as a static line. This form allows you to use the wire at the length that it was anchored at without reeling it in. This is how you see people using centripetal force to "swing" around clock towers or under tree branches with the use of gas or gravity while their wire remains the same length. It is accomplished by simply clicking
nothing. Easy Day. Best example would be these two guys flying past this Titan,
especially that second guy.
Wew past the easier things I guess. The next few are pretty much pure speculation, namely from forum discussions and my own interpretation of how the 3DMG is controlled. For this I'll just touch on the remaining controls and explain what others and/or myself believe they do.
Starting with the "Gas Trigger" or what I called a "Handle" in my last IC post. The Gas Trigger is the large trigger in front of the rest of the controls as seen in the diagram above. It controls the output of gas at the grip of the user, the lighter it is pulled down the less gas it outputs and the harder it is pulled the more it outputs. This allows for a user to regulate the amount of gas that is used in order to move and thus either save or expend gas as they see fit for their situation. This is mere speculation on the part of a few forum discussions and I'm not too sure on it as in the scene when Mikasa is using too much gas she is not touching the handles whatsoever. But for lack of a better explanation of what this trigger does and lack of any other device to control the use of gas that's what I've settled on for this.
Alright, we'll hit the Traverse Control here. This control has been pretty well established although it seems to swap between whether or not it is the top control or the bottom control and is not very consistent from the forum discussions I was reading. As such it is possible that the actual actions are accidentally switched between the Traverse Control and the Blade Release, although it is safer to assume that the act of traversing would be delegated to the control closest to the thumb (The bottom control) and it is very obviously show in the Levi OVA series during the first encounter with the Scouts.
(Why he uses the front handle and bottom trigger is beyond me, hence why I said a lot of the use of these controls is speculation.)
The Traverse Control does what is in the name, it controls the traverse, or horizontal movement, of the two pieces that both house and fire the hooks. It can be assumed that if the Traverse control is switched to the back position that the hooks are aimed forward as this seems to be their default position, and if pushed to the full forward position they are aimed at 90 degree angles to either side of the user. They are controlled separately by each control grip as is every other aspect of the Gear. These switches are also considered to not be just a simple "on or off" control, and instead can traverse the hooks firing position at any angle within the 90 degree horizontal arc as the user sees fit by slowly sliding the control forward or back ever-so-slightly to aim as they see fit.
To be clear these next two are my interpretation of the two controls and actually go against what forums believe they do, but I think those people just didn't look hard enough.
The next up would be the Vertical Traverse Control, or the hammer seen to the rear and above the handle. This control seems to control the vertical traverse of the piece that houses and fires the hooks to some extent. How much it can traverse is widely up for debate although it's got to be a considerable amount when considering that a user can be crouched on top of a horse and fire the hooks at nearly 90 degrees up or practically parallel to their upper-bodies. I will say that a lot of forums believe that the hammer is actually the blades release, but I don't buy it as why the fuck would you put the control to release your only weapon in such an open and easily disturbed position. Also there is the intro scene with the Scouts that has one of the Scouts holding the hammer in the back position while mostly sitting on a horse with his torso facing toward the ground and yet the hook fires on vertical angles.
Last would be the Blade Release. It's can be assumed to be a switch as it only needs two functions of either holding or releasing the blades (on or off). Push it forward and you release your blades. Leave it back and the blades are locked in place. Loading of the blades seems to have no correlation to the switch being in the back or default position as seen by the fact that many people reload blades on the move and rather forcefully. Likely the blades "drop" into a position and are seated with a locking mechanism that can be released with this switch.