As I didn't already see a how-to post for changing the air filter on ST1300s, I thought I'd post some pics. It's a pretty straightforward process that should take ~60 minutes, start to finish–especially if you've never done it before. Note: Perform these steps on a near-empty tank.
Step 1) Remove seats and the two 8mm bolts toward front of tank.
Step 2) Loosen the 10mm bolt and nut in the image below. They are located in front of the seat-height adjuster. This will allow you to slide back the tank an inch or two so that it clears the bar risers in the next step - make sure to push the seat-height adjuster towards the rearmost slot called the maintenance slot.
Step 3) After sliding tank back, gently lift the front of it being careful not to scratch/ding it against the bar risers. I used a bungee cord to hold the tank in a lifted position. (See image below.) You can also temporarily remove the retaining cable to get more clearance.
Step 4) Remove the nine Phillips screws holding the box cover on. Note: As others have suggested, it's probably best NOT to remove the two front screws. Doing so could risk dropping them into a hard-to-reach area. Also, there's a small wiring harness that's easy to disconnect, which will allow you to completely remove the box cover. I did this so I could wipe clean the underside of the cover.
Step 5) With the box cover removed, you can remove any visible debris and wipe clean any oil residue. I used the home vacuum cleaner with crevice wand to remove remnants of a dead bug.
Step 6) Proceed to swap the air filter then reassemble.
As you can tell, I used a replacement from Emgo (http://www.amazon.com/gp/product/B00...?ie=UTF8&psc=1) and did not use any type of grease to help seat the filter. (Others may suggest differently.)
Hope this helped.