I basically know what they do to an extent, but I'd like to get some of the movie buffs to answer this (mainly Shake, Solo, and Willco).
I'm not talking about the coaching/directing of the actors; I get that part. More along the lines of the rest of the film. Like the camera; I've read places that director's control the camera, but then I've read other places about movies with actual camera guys who do the shots. Directors bring the script to life, but I want to get more insight
The director is the thread that ties everything together. He works with the actors to get them in the right frame of mind for the scene they are shooting, and keeps making little tweaks until the actors give the performance the director wants. He also works closely with the DP/cinematographer on many levels, from the big issues like what sort of shots he wants, to the composition of shots, to the lighting, to more minor things like color filters and image saturation. Its the cinematographer's job to capture the images, but its the director that is telling him what images to capture, and in what manner to do so. Certain director's like Ridley Scott and Michael Mann are almost DP's themselves, as they shoot a lot of stuff themselves. The director can make unsanctioned changes to the script too, if he feels certain changes will better suit his vision. If its a film with lots of effects, then the director would spend a lot of time in pre-viz, communicating with ILM/WETA/etc exactly what he is looking for. Once the film is shot and in the can, and things shift into post-production, the editor and the director will get together and piece the movie together. The editor is making the cuts, and the director will often be choosing which takes get used.
Also would the director be the one to say hey, I want to use a tracking cam or whatever for this scene?
Yes. As has been mentioned, Marty is pretty much the king of the tracking shot. Most of his films feature at least one major one, and some are amongst the most famous in film history. Dont look to The Departed for one, though, as you wont find it. Scorsese ditched a lot of his usual techniques in that film.
Ok this makes sense. But like for instance, there's a lot of discussion about the particular style of directors, but how is this translated to screen? With Leone I've read alot about some of his style, and it's visable in movies like Once Upon a Time in the West; the close in shots of faces and such.
That's pretty much how it is translated. Leone's style was filmmaking that bordered on still life photography. He loved a nice wide frame, with very little motion going on, and very little clutter in the composition of his shots. Then he liked to hold these shots for an extended period of time. His other stylistic trademark, which is on pitch perfect display in my favorite scene of all time in film, the cemetary shootout in TGTBATU, is the juxtaposition of extremely tight closeups and long shots. He uses them in rapid fire in that scene, to great effect, matched up with Morricone's score.
Leone decided how to shoot the movie. I believe Leone was a guy who edited movies in his head and he already had sequences thought up, right down to the close-ups of the eyes. I believe he was also one of those guys who liked to work behind the camera. He would make sure his cinematographers knew the shots he wanted, and he would work with them until he got them.
Yup. The other unique and awesome thing about Leone was with respect to his use of Morricone's scores. Most filmmakers shoot the movie, then the composer comes in, and crafts his music around the rough cut of the film. This standard practice is what Leone and Morricone did on Fistful of Dollars. However, for all their other film collaborations, they worked in a truly unique way. Leone would have Morricone compose, conduct, and record the score before filming ever began, and then he would craft his sequences around Morricone's soundscape. He would blare Morricone's music on-set to get the actors in the appropriate headspace. A brilliant scene like the shootout in TGTBATU was 100% a product of Leone marrying his shots and cuts to Morricone's amazing score.