The King's Indian Fianchetto Variation is reached by several move orders, but let's begin with the most straightforward.
Let's agree on this as the starting position for the KI Fianchetto Variation. The Queen's Knight hasn't been committed yet, unlike the other KI mainlines, and the light-squared Bishop is coming in on the long diagonal, instead of to the usual e2 or d3. White is likely going to push the e-pawn two squares as in other variations, but even that's in question. This variation usually lacks the wholesale assault by Black on the White position due to the extra protection afforded by the Bishop, and the center will tend to be more fluid than in the other mainlines (it's more difficult for Black to focus an attack on the kingside when the center is not closed).
Now White usually plays 6.O-O, but note that because the KI is a hypermodern opening Black is not tying White down to any particular move order. Black has several moves, with the principal being 6...Nbd7. Others include 6...Nc6, c6, c5, a6, Bg4, Na6, and Bf5.
6...Nbd7 The Knight is not ideally placed here, of course, but it's going to support Black's play into the center at e5. In response, White has the major move 7.Nc3, the often-played 7.Qc2, and the minor moves 7.b3 (see G124) and 7.d5. We'll look at Nc3 in the main, consider Qc2, and handle the other two moves in subsequent games.
8.e4 White also plays 8.h3 here, but it has little independent significance. Black now plays 8...c6 almost half the time and 8...exd4 a little over a quarter of the time. The other two common moves are 8...Re8 and 8...a6. After 8...c6, play may continue 9.h3 Qb6 10.Re1 exd4 11.Nxd4 Ne8 and Black is okay. Continuing, 8.e4 c6 9.h3 (9.b3 Re8 10.h3 exd4) 9...Qb6 10.Re1 (diagram)
II. 7.Qc2 e5 (the alternative is 7...c6 and it may be objectively as good 8.Rd1 Qc7 9.Nc3 e5 with a slight advantage to White) 8.Rd1 Re8 (8...Qe7 Nc3 9.c6 e4 10.exd4=) 9.Nc3 c6 10.e4 (10.b3 and now while 10...e4 has been the move of choice, this position deserves closer attention) 10...exd4 (10...Qe7 and look particularly at 11.b3 or d5) 11.Nxd4 (diagram) and Black is okay.
Now a couple of games.