There are at least a couple of ways to do this mod. Both involve opening the air box up, tank off, etc. Once inside you will see a piece of rubber - commonly called a snorkel, it is glued into position. You will see it is designed to funnel air inside the airbox.
One mod involves just pulling the snorkel out and running the bike without it.
A variation of that involves removing the snorkel and opening out the blanked off side with a craft knife or similar. Then simply refit. No need to glue as the ends of the snorlel are designed to " clip " into the side of the airbox.
Apparently this second mod is how the Speed triple breathes as standard. For some reason Triumph restrict the air intake arrangement in the Tiger.
I did mine the first way. Then thinking better of it, changed my mind and refitted the snorkel after opening it up as stated above.
It's hard to tell the exact power gain without putting it on a dyno. I also have the TOR can and tune fitted. With all these mods the bike must be making similar power to the Speedy. Sure feels like it.
Hope this all makes sense.
ps. Bung a K&N or Pipercross air filter in while you are at it.