It depends on the type of production. If it's say, a documentary where you have hours of unscripted footage; a drama where the shots are organised by scene, shot and take and you are working to a script; or a short-form piece like a TVC where you are cutting a small amount of footage down to 30 seconds.
That said, the process of editing is basically one of organisation, and it involves getting to know your footage, and then making decisions about what helps the story and what doesn't.
Getting to know your footage can involve any or all of these steps: logging - actually going through and taking notes of what happens when in the footage, choosing good or NG takes and marking them up in your project, sorting into bins, and even just naming your clips in the project. Actually, I find that naming your clips is one of the best things you can do to get your edit started. The more time you spend watching and organising your rushes the easier it is to cut them.
From there you need to start deciding what's in or out. An assembly edit is the first step – where you put in all the shots in rough story order, without worrying too much about matching cuts or sound or any finesse. At the end of the assembly you'll have a good idea of what your coverage is like, and this can sometimes be the point where you decide to shoot more footage if you can. At this stage the timeline is usually way longer than the final cut.
Then it's a process of finessing the cut, starting with the rough cut. This is where you focus on what shots are needed to tell the story. You may go back to your rushes to find extra angles, or cut-ins and cut-aways to help the cuts work or to improve the storytelling. You won't be doing any sound or colour tweaking, titles, effects or any other malarky at this stage. You may be using placeholders for effects shots etc.
From there it's a matter of making the editing seamless; making good motivated cuts, watching the pacing and rhythm. This is your fine cut, and it's the last stage before you lock down your edit and start doing the online stuff. If you're cutting to a set time this is when you might be making hard decisions about what's not absolutely necessary, and tightening up the cuts.
The "online stuff" includes adding graphics and effects, titles, music, and lastly colour grade and sound mix. Colour grading is where you firstly balance the colours between shots, and then give your shots the look that you want. Sound mixing is similar: you try to make the sound seamless between shots in a scene first, and then add other sound elements like sound effects atmos and music.
In reality there's really not hard division between the assembly, rough and fine cuts, they flow into each other. The trick is not to start worrying about getting a cut exactly right in the assembly edit because you might want to lose the shot altogether later on, so you'll be wasting your time. The idea of the assembly and the rough cuts is to focus on the whole piece without getting bogged down into individual shots.
I find that non-linear editing does make it very easy to get sidetracked into doing fine cutting too soon (when you cut on film you didn't want to cut scenes too short too soon, because it was a damn nightmare finding those one-frame trims in your trim bin and sticky-taping them back on).
There is usually a boundary between editing and stages like colour grading. You want to have your shots "locked off" before you start grading or you'll waste a whole lot of time going back and forth. Though recently colour grading packages have started to have the ability to dynamically respect edits that you make after starting the grade, so you now have the option of grading and cutting in parallel.
Effects too will often require the edit to be locked off, so that you don't waste time doing work on parts of shots that aren't used. But again, you may have to do a bit of to-and-fro between effects and edit. Packages like After Effects and Premiere work well together: if you have shots in your sequence that require effects work you can export them from the timeline via dynamic linking, so that you can watch the effect in your edit without having to render out to file.
There is no set-in-stone way of doing this, everyone and every project needs an individual approach, but this should give you a general idea of the way I like to do things.
