Most of you with a 2013 Triumph Daytona have probably read this article about fairing removal: https://www.triumph675.net/forum/showthread.php?t=894
There are some differences for the 2013 model, but the above article is still a good read.
Step 1: Remove dash inlay panel. There is only one bolt to remove. This piece sort of snaps in place where the carbon fiber meets the white trim piece. Just gently wiggle the piece and it should pop out.
Step 2: Remove bolts from top of fairing. There are like four bolts to remove.
Step 3: Here is an overview of all the bolts/screws that need removed. Note: The 4 holes on the left are these plastic snap in screws. Gently unscrew these. Once the screw comes out, pull the housing for the screw out with your fingers. Also note: You do not need to remove the bolt that holds the turn signal in place.
Step 4: Once you have all the appropriate bolts/screws removed, the fairing should slide slightly toward the back of the bike and come out very easily.
Step 5: To re-install, pretty much do the reverse of what you did above. The only problem area I had was putting the inlay panel (see step 1) back in place. This has to be lined up perfectly, otherwise, when you try to screw the bolt in you'll just keep popping the metal clip/nut out. I think I did this about 10 times before I realized that things have to be lined up perfectly so that you don't pop the metal clip/nut out of place.
If you look at my first photo, I actually took this photo when I was putting the inlay panel back in place. Notice my hand position. I was pulling the inlay panel toward me so that the holes would all line up properly.
In summary, it is pretty straightforward to remove the fairing. Hopefully this will help on your first disassembly.
As my pappy used to say "If it comes apart with nuts and bolts, it goes together the same way."