I long ago started making the G chord as Glenn describes above, but I don't find it necessary to skip/damp the 5th string; I play it at the second fret with my middle finger.

Now, I am a fingerpicker, so I'm usually playing no more than 2 or 3 strings at a time, anyway ~ except, of course, when I want the full chord, in which case I'll "strum" with the thumbpick.

My arthritis is at its worst in my left pinky finger ~ since I can't bend it nearly as much as I used to, my middle and ring fingers reach for those two lowest G-chord strings at more of an angle than is ideal, making it a little more difficult (but not impossible) to avoid muting the open D string.

To compensate in some situations, on some songs, I've begun playing the G chord yet another way, new to me: wraparound thumb to fret the bottom E string at the 3d fret and to mute the A string with the tip of the thumb, plus the middle finger to fret the top E, sometimes along with the B string as well, also at the third fret. This is not particularly useful when switching quickly between G and C and playing melody/treble notes with the pinky, but fits very nicely into some other arrangements, especially when transitioning from first position up the fingerboard and/or back again. And of course, playing that "D" note on the B string as part of the G chord, instead of leaving the B string open, is sometimes a preferable sound.

PS: Incidentally, I don't think of the 2-strings-with-one-finger version of the C chord as Patrick Costello's ~ I think of it as Rev. Gary Davis's. The Rev had a pretty huge pair of hands, and could hold down those strings with a single finger much more readily than most of us could. He served as mentor/teacher to a number of then-young New York folkies who passed on their lessons (including how to make that chord) to the masses via songbooks w/ tablature and, later, with tapes and videos.