When you enter a room, the first wall you see is the wall you start on.
Upon starting, I cut a block of scrap wood that mimics the rise and run of the crown.
The dotted line shows the square back that has been cut off help set the block in the corner, since the drywall corners are not square.
Go around the room with a stud finder if you have one and locate all the studs if the crown is wide, like 5" or so. If the crown is narrow 4" or less, the top plate will be the area you nail into, that should be 2 1/2" of solid wood below the ceiling. That can be checked in time.
If you do have wide crown, use the stud finder to locate all the studs and mark them with blue tape, using the block that depicts the rise and run to set the tape below the bottom edge of the crown, so when the cut crown is set in place, it will fit both the ceiling and wall.
When measuring, do so at the bottom edge where the blue tape is on the wall. Cut the first piece not square but slightly shorter at the top, so the bottom engages snugly. The loose fit at the top will be covered by the next piece. Set the crown to the wall so the bottom edge is on the top edge of the blue tape marking the studs, if you did it that way. I failed to mention, if you are using a narrow crown, the blue tape can be set to the wall about 2' apart, no need to find the studs. A little "self help" I add, I set 2 nails on the wall, near the corners,about 1/4" above the blue tape, and use those to support the ends of long crown when I am working alone. I have the crown in the middle, and the 2 nails supporting the crown, insures the crown is in the corner where it needs to be. If it drops down, and you nail the center, the crown may be shifted to one side and will scratch the wall getting it in place. Nail off the the crown, EXCEPT the last 2 feet. Leaving the last 2 feet free on either end, pull the temporary nail supports, making sure the crown naturally sets somewhere close to the blue tape marker. This will aid in fine tuning the cope joints when the next piece come into play.
If you have never coped a joint before, you will need to get past a learning curve. All coped cuts after you cut the initial 45 degree miter, will need to be severely "back cut". That is, do not even try to cut a cope square to the piece it meets, it will only cause you sorrow. Use a few short pieces to get the hang of it before you start cutting the real deal. Purchase more crown than you need specifically for this, 4-6' should do it. You have you cut offs to practice with too. The severe back cut lets the sharp coped edge to cut into the adjoining piece, if not that, the edge is so thin that is will deform just a little to make the joint really tight. You can measure all of the crown ahead of any cutting, if you choose. If you do so, I find for some reason all the coped lengths I cut are about 1/8" too long, which is fine, better too long than too short. There are other ways to measure that are obvious as well, so I will leave my 2 cents worth at that.
When setting the first coped piece, and it is long enough, take the crown in hand about 4 foot from the coped end and set it in place. The end will droop down ideally. You want to ram the crown into the closely placed first piece you have already set so the back cut edge drives into the first piece. This trick requires both piece are on the wall as close to the finished height that they can be. Hence the blue tape. When done nail off all the piece except it's last 2 feet. The third piece is done the same way.
The reason for the last 2 feet still free is so the crown can be moved to get the joint snug all along the cope. Typically the gap is at the top, this is fixed by using a short, square cut 2X4 to drive BOTH pieces up to the ceiling to tighten the joint. THEN nail the last 2 feet.
The last piece has only this difference, coped on both ends. This one I prefer to be an 1/8" too long so I have room for fine tuning. If the piece will fill well on both ends, and it is bowed out say 4" from hitting the wall in the center, push it in place, this will do he same action as driving the cope into the adjoining piece and get the joint really tight. If the last piece really is resistant to going in at the center, check which end looks the worst, first making sure is in the right place first, cut to compensate and shorten, re cope and reset.
So much for the short answer....