The best places to obtain autographs from A's players are shown on this page.
For a more detailed overview, read the Getting autographs section on the Hohokam Stadium guide page.
Where the tarp is stored at Hohokam Stadium -- in front of section 113 and spanning some of section 115 too -- is where you want to be for the best pre-game autograph opportunities with A's players, whose dugout is close to the tarp.
Prime signing time is approximately 20 minutes before game time, although 30 minutes before first pitch is when players start to warm up out on the field and sign autographs before and after they stretch, etc.
Fans beyond the tarp are not shut out. Although typically less players sign down the line past the tarp and further away from their dugout, it would be unusual for some of the A's not to come over to those waiting in section 115 or 117.
The epicenter of autograph activity inside of Hohokam Stadium is found outside of the team's clubhouse door, which opens up to the concourse at the end of the first base grandstand. This is where you want to be after the game.
For roughly 25 minutes after the last out is recorded, fans can line the barricaded path set up outside of the Oakland clubhouse door, which players must exit to head to their parking lot or, in the case of minor league guys, to the shuttles that take them to their clubhouse at the organization's complex about a half-mile away.
Those waiting along the path will have the closest encounters with the least amount of competition from fellow fans, which equals the best chance for acquiring autographs on stadium grounds. And the guys signing in uniform after the game are usually minor league players, as the regular roster guys have showered and changed into clothes by then. Depending on the day, some of the "name" players will already be gone by game's end, although there's usually a few players in their street clothes mixed in with the departing uniformed minor leaguers.
Unfortunately, this great post-game autograph area "closes," or is at least cleared out by security staff, within 30 minutes of the game ending, as 30 minutes after the game is over is when the stadium's gates are closed.
So to sum it up:
Before the game: be down at field level, behind where the tarp is, in section 113, which is very close to the Athletics' dugout.
After the game: stand at the barricades lined up outside of the clubhouse door, which is at the end of the first base grandstand.