I usually can't FRED unless I'm in the mood for FRED. I have to "feel creative" when I'm starting a new mission, otherwise I either can't make progress or the mission "rough draft" is very mechanical and not much fun to play. I need a "spark" before I can start a new mission.
Getting in a FREDding mood can happen several ways. Sometimes it just happens, which is the easiest.

Sometimes, all it takes is reading some FS stuff or listening to FS music. Other times I have to play FS for awhile before I get in the mood.
Once an idea hits me, I'm set. How I actually start FREDding varies. If I have a particularly solid idea in my mind about how I want a briefing or some dialogue to play out, I might write that first. I'll probably also write a few notes to describe what happens in the mission, just to keep things straight.
The order in which I add stuff is flexible, and most of the time there's quite a bit of overlap between placing ships, adding events, and adding messages. Usually I'll add the major players first - e.g. if it's an assault or defense mission, I'll add the capship or installation that's in the center of the action. If it's an escort mission, I'll add the ship(s) or convoy being escorted. (The first thing I did when making the ST:R mystery mission was to arrange the convoy freighters and give them waypoints.)
Every so often I'll start out by spending quite a bit of time on one particular feature until its exactly the way I want it before doing the rest of the mission. One mission late in ST:R was done this way: I spent several months perfecting a particularly complex series of events and AI orders for a bonus objective that appears two-thirds of the way through the mission, then built the rest of the mission around it. (I'm quite proud of this objective, as it incorporates a bit of noncanon Freespace history as well as some complicated event scripting, AND it's only triggered if you do well in the middle third of the mission. I'm eagerly anticipating the reactions to it.

) But most of the time I add stuff in chronological order.
In general, I'll add all the stuff associated with an object or concept before proceeding to the next one. If I add a capship, I do its arrival/departure cues and waypoints first and maybe give it a wing or two of escort fighters. If the arrival of a fighter wing is accompanied by some chatter, I'll write the chatter. If a transport needs to capture with a capship, I'll do all the docking-related stuff in the order that it happens: dock order, dock message, capture chatter, IFF change, and goal and directive code. Unless the mission is really complicated, I'll try to do the whole mission this way, or at least a rough draft of it. This helps me keep the whole mission in my head and keep track of which events and ships affect which other parts of the mission. Then it's time for playtesting.
The playtesting process is pretty much "keep refining everything until you're happy with it". I play the mission, pausing frequently to take notes, until I reach a point where it's necessary to add the changes before proceeding further. Then I switch to FRED and go right down the list, adding changes and fixing bugs. Once that's done I switch back to FS. The process tends to be very "loopy" as I test the mission, make changes, test again, make changes, and so on, each time getting a little farther into the mission. I try to refine all aspects of the mission - messages, events, ship placement, ship balance, etc. - in parallel, as it keeps the mission feeling coherent. If I focus on only one aspect of the mission at a time it sometimes causes the mission to feel segmented.
At this point I do the briefing or debriefing (it's a toss-up which one I do first) if I didn't do it before the mission. When doing the debriefing, I've recently found it helpful to add a stage for each possible outcome of the mission, with a few short words to describe it such as "ship X destroyed, say congrats" before actually writing the text. This helps ensure that I don't forget an outcome while I'm writing the debriefing text. (Depending on the mission, the briefings, debriefings, command briefings, and messages can easily take several hours of composing and rewriting before I'm happy with them. I'm not content with just writing stuff that simply explains what's going on; I want it to have the proper
feel for the mission.)
I don't do backgrounds at all; I hate doing them with a passion.

So I just look through other missions until I find one I like, then I plop it in with cut & paste. This is usually the very last thing I do, and in DEM it wasn't even done at all.

I typically work on only one mission at a time until it's done, unless I run into a huge problem or a delay of several weeks that causes me to lose my momentum. In that case I'll sometimes FRED another mission to completion before returning to the original one.
So that's the process, in a rather large nutshell. As for the rest: I like the environment to be peaceful and free of distractions, as I work best if I have a large, uninterrupted block of time where I can get a lot of stuff done; though it's helpful to take a break or sleep on a problem if I can't figure it out in a reasonable amount of time. If I'm making rapid progress I prefer it to be quiet, but if I'm thinking of plot points or debugging I sometimes like to listen to the FS music. Lighting typically doesn't matter much; I've FREDded in both daytime and nighttime.