One of the first things I do before I receive the music to be mixed is discuss with the artist the intentions of the song. I like to know more about their vision, so that I can hopefully help them realize this goal.
It's never good enough just to present a great mix. It is an aesthetic goal that is both abstract and seemingly elusive. The idea that a person could "click" so well with another and develop a mutual trust in pursuit of the same aspiration is amazing. Ultimately, the mixer's role is no different than that of a bandmate. When the chemistry is apparent between the artist and mixer anything is possible.
So try to spend time with the artist prior to the mix process. It doesn't have to be a formal environment; it can be as simple as grabbing dinner or a beer a couple of hours beforehand.
Once you receive the mix listen to the producer's rough mix of the song. Try to listen without prejudice. It's so easy for a mixer to become arrogant and think, "My god, this is horrible. I can't listen to this garbage. Just let me get my grubby hands on it and I'll make it great." Perhaps this is true. The objective, however, should be to listen to the producer's "representation" of the mix from an artist perspective. If they intended for this version to be a perfect sonic realization then they wouldn't need you to mix it, right?
Try to be objective about what you hear versus what you can contribute. Take notes and intermittently reference their version throughout the mix process.
Another aspect I prefer to perform myself is the post-editing. Often, there may be elements of the mix that still need to be edited before you can really get down to mixing. Maybe it's a tom hit that resonates too long or a guitar accent that could be tighter.
In doing this you get to absorb yourself in the inner workings of the song. It can give you time to become more familiar with the arrangement and various queues. These queues can be very critical in how you perform dynamic automation maneuvers.
Once the mix has been completed per your standards, go back and reference the original reference again. There may be things that you now feel are much more similar in approach and will be glad you didn't disregard them.
Allow the artist or producer to review your mix and offer recall notes.
The crux of this "How To" is that if you take the time to become absorbed in the music and share the same vision as the artist, the more easily the result. If everyone is on the same page from the onset, you are less likely to endeavor into the back-and-forth recalls inherent in this profession. Everybody wins.