2. d4! 
holding the center
There are several developing plans, it depends on black...
He usually continue with e6 and Bb7. White can play i.e d4, f4 and eventually c3, or more classic Nf3, Nc3, or ambitious f4, d4, c4, which is dubious.
Be creative, that is why the Owen is played.
Quack, quack!
I always found playing the Owen to be too limiting and inflexible as Black.
The fianchetto on the King's side is much easier to play, at our level.
Partly it's because Black's natural lever-move f7-f5 (to cooperate with the fianchettoed b7-Bishop) is much harder to safely arrange than Black's usual lever-move c7-c5 to cooperate with a g7-Bishop in those systems with a King's side fianchetto instead.
I always found playing the Owen to be too limiting and inflexible as Black.
The fianchetto on the King's side is much easier to play, at our level.
Partly it's because Black's natural lever-move f7-f5 (to cooperate with the fianchettoed b7-Bishop) is much harder to safely arrange than Black's usual lever-move c7-c5 to cooperate with a g7-Bishop in those systems with a King's side fianchetto instead.
who revived a thread from 2007 lol
actually, that flexibility of g6 is why a lot of people find it harder, not easier to play . In the owen's your main counterplay in most of the non-hippo/ funky knight tour lines basically, revolve around c5 and d5. In the modern, the extreme flexibility means the right continuation to play in each individual position is a lot less thematic. Considering that the d pawn is already defended by the queen, getting good counterplay agaisnt a solid center is not trivial, and white can choose, to hold, bypass, or keep tension.
say you have 1.e4 g6 2.d4 bg7 on the board as the black side, now what?
you have to prepare agaisnt the natural 3.nc3, the solid 3.c3, the bold c4 and f4, triple pawn center ideas, the lines, where white will hold the tension on d4 with nf3 and try to get a sicilian esque position, lines where he might push benoni style, lines where white is prepped and takes on c5 etc.
in the owen's most of the lines you really have to worry about involve holding the central tension at first, and e4-e5 at some critical point. Whether they go bd3 and qd2, or bd3 nd2, or nd2 without bd3, or lines with early f3, or nc3 and nge2, the theme is almost always the same. The main threat is white holding the center and then releasing with fury e4-e5 at the right moment. much easier to study.
Continuations?