How do you approach mixing?

Yep. Start with drums. I think of it as a pyramid - drums and bass on bottom, and then later up in lesser prominence.

My first step is to select all and bring all the faders down

I tend to start with snare, then kick, rest of drumset, bass, bass&kick, bass&drums, etc.pp. ..., vocals, vocals&guitars/keys, full mix.
But this is simplified. I always have the picture of the whole mix, and what i want to achieve, in mind. Therefore, i may flip to whole mix and back in the whole process of mixing from time to time.
I set all faders to the same below zero dB level from the start and have a sincere look for conventional gain staging, i.e. i use trim knobs, watch out for unwanted clipping etc. and i re-level while eq-ing.
Then i use the fader levels for decisions on the sound of the whole mix, level automation etc...
Well, it does not always work out like this, but i aim at doing so.
This way most of the time i can *see* which choices i made for individual instruments concerning the complete mix. E.g. if i decided to turn down hi-hat or one of the guitars in the mix, it ideally reflects in the fader position. Well, if you don't use an at least *somehow* similar kind of practice, where fader position does have some kind of meaning, at all, you could happily dump all faders and use knobs instead, like on the old tube consoles...
I think most of the time i just follow the best practices that i learned in the analog 80's/90's, aiming at non-clipping relatively clean results.
Here in Germany most of the artists, when it came to studio or live work, asked for "clean" sound, "no effects", no "overproduction". Everybody was concerned about noise, distortion, muddy sound and digital artifacts.
But i also learned, that, given that you have a good sounding console (or whatever analog type of amp stages and eq), you *can* do all kind of tricks that wouldn't work otherwise. Like driving preamps into saturation or even clipping, using eq for all kind of stuff it was not build for in the first place...
Careful digital gainstaging therefore is not different to what careful analog gain staging was like.
Means - it aims at avoiding saturation=coloring and distortion/clipping.
Now, what made analog mixing that much fun was, that analog saturation and clipping can sound quite good and that there was gear, that you could hardly make sounding bad. So, if it clipped but sounded good, why not?
Digital clipping on the other hand is quite nasty, and the problem is - if you don't give attention on proper gain staging from the beginning, you will have a hard time finding out what makes your mix sound bad.
Especially if you are mixing a live event. I guess this is what gives digital FoH consoles such a bad reputation mostly...
The only DAW i like for behaving like the analog consoles and therefore giving back the fun of intentionally breaking the "gain staging rules" is mixbus. It is not because of the quality of emulation, eg. Nebula could do the same. But it is that you do not have to watch out for digital clipping inside of the complete console, which is unique for a DAW.

I really learned the most i know about mixing from analog mixing under pressure (time). Which i can seriously recommend for getting a fast pace in achieving what you aim for. Ideally FoH mixing. (Making fast and fearless decisions and do the best you can because many people *will* hear the difference - immediately...)

I approach with a ten foot pole, then attack carefully. It's all analog console and outboard, just like in 1975.

Then I let my cat walk across the console to add interesting mixing choices. It's usually good to break habits.

If I like what I hear, kitty gets a cat treat.

Someday I might let the cat do the entire mix. Couldn't be worse than some of the stuff I hear these days...

Build a mix like you built the recording:

Guide vocal and guide instruments in for the start, then you recorded the rhythm section so you bring that in... then the guitars, then keys, then acoustic overdubs, then leads, then the lead vocal and finally the bvox. Then start bringing down the loudest thing in the mix over and over again until you hear everything clearly. then start other treatments. Groups? Drums, backing vocals, maybe rhythm and acoustic guitars. that's it.

Brilliantly stated.

For me it starts with getting to know the song, if I can I will start hearing a client live, if not I try to listen to all the tracks, find what's there, often there is something that will just make a track hidden. So much of my mix comes in on tracks where I didn't do any tracking, and is referred because somebody just got in over there head.

More often than not drums create the space in which a track lives.  It's the way a room (or a faux room) reacts to the percussiveness that tells the listener where we are.  So after getting some basic levels and panning on everything I dig deep into the drums and then build things around that and try to be open to change as I go.  Everything is important, but it helps me to understand that drums provide the setting and vocals provide the conversation--in a way everything else revolves around those two elements.  Honestly I wouldn't want to get too locked into a specific mix order such as bass or guitars first -- to me that would limit creativity.  

Well, Guitar,
i just integrated my old US-2400 into our setup again and wondered, how i could work without it (it is basically a usb class compliant Mackie Control emulation with 24 flying faders + master fader, jog shuttle wheel, transport section like on the old tape machines, lots of keys and a joystick etc.pp.....and very silent on the faders.)
Try to lend an MCU and see, if you can work faster with a control surface. For me it makes a huge difference, because i come from the analog mixer originally. Many younger guys don't get the point of control surfaces because the are used to use mouse control in the first place...
But if you come from analog - control surfaces are simply great.

BR,
Martin

Then there's the Hugh Padgham approach of putting up the vocal first and building everything else around it...