The fixtures for the upcoming Premier League season have been released, and Arsenal will face Sunderland at the Emirates Stadium (presumably, until TV have their way) on the 18th of August. Arsenal's fixtures, though, get trickier after that. Only four of the first ten fixtures are at home, with Arsenal having to travel to Stoke on the 25th of August and Liverpool on the 1st of September before the first International break. After that, in the first ten fixtures, there's a trip to Manchester City following a Champions League week and a home match against Chelsea.
The first North London Derby is at the Emirates, and is on the 17th of November. Arsenal haven't been dealt a very kind January; they face Southampton at home and then have a run of Manchester City, Chelsea and Liverpool in the league. Last January, Arsenal had a run of 1 point out of 12, and if they are to be involved in the title race this season, you expect that they'll have to take more points from those fixtures.
All of that, though, is down to the quality and health of the squad, something that'll be tackled in the coming weeks. For now, it's a bit pointless to speculate about where Arsenal can pick up points, so instead, start putting fixtures in your calendar/diary/wall chart, and make sure you have access to the television for those weekends.