The Tuna auction, which I missed, starts at 5:20am. I heard that it was quite a sight, and I might try to catch it next time. Please post if you can add any info regarding the auction.
I decided to walk there which at 1.8 miles only took about 35 minutes at a leisurely pace. You could take the Ginza line, but it still involves a lot of walking and won't save you too much time.
It's easy to get there, but the lack of English street signs makes it a bit tougher. If you can, print out a map before you go. An iPhone may be a handy too. To walk there from the Intercontinental, I took the following route shown on the map below:
As big as this place is, you'd think that you'll have a huge sign saying "TSUKIJI FISH MARKET", but as far as I could tell, there wasn't any such sign. You'll have to go through one warehouse area that held produce items before getting to the heart of the fish market. So it kinda feels like you might be in the wrong spot, but fear not. Watch out for the turret trucks!
Once inside, just walk around and enjoy the sights, sounds and smells. The workers there won't pay much attention to you since they are very busy, but they are still friendly, and didn't mind having their picture after being asked.
Enjoy your tour!
Here are some of the shots I took: