To expand a bit on the good answer already given:
- Slope - 25-45 degrees is a good broad suggestion, but your region of the country will have a big impact on this. Maritime snow is wetter and stickier, so tends to be most dangerous at steeper angles. Transitional and Continental snow is less wet, so has a most dangerous slope range on the lower end of the scale. Find out more specific information from the avalanche center closest to your location.
- Any rapid changes to snow position, temperature, or sun. Lots of fresh snow, lots of wind moving snow around, a rapid change in temperature can all increase avalanche danger. The avalanche dragon hates change, and it makes him angry. Stable conditions are less likely to enrage him.
- "Whumfing", cracking or visible settling. All very serious danger signs.
- Avalanche chutes - look for places where avalanches have happened in the past, by looking for debris, or places where there are no big trees all of a sudden. But also look for evidence of recent avalanches. Check high slopes above you all the time - if you see a few fresh looking slides, that is a huge danger sign.
Forgetting the snow for a moment, remember that an avalanche fatality requires two things - snow conditions, and a person to be there. Avalanche deaths are primarily men, aged 20-29, who are experienced skiers. Not because avalanches like these people more, but because they are most likely to find themselves in a risky location, doing a risky thing.
Group dynamics and decision making will have a greater impact on your survival than snow science (though that is important, too). In nearly all avalanche fatalities, the investigation finds that someone in the group either identified the hazard, or had sufficient training to identify the hazard, and yet the group did the dangerous thing anyway.
Evaluate your group and make some rules:
- Everyone has veto power on dangerous situations.
- Make several plans. Instead of "we are gonna ski that wicked bowl", decide on a few options in different locations so if one area looks dangerous you are comfortable changing plans.
- Don't get lulled into a false sense of security by good weather, or having an "expert" in the group. Everyone's eyes are open, and everyone discusses the situation as they see it.
- Don't get macho - if the conditions don't feel right, its fine to turn back. When they say "go big or go home", remember that sometimes it's just fine to go home. ;)
And finally - take a class. Depending on where you are, there are probably some good Level 1 or introductory courses available free or inexpensively. Bring your friends, too - being trained on avalanche safety doesn't make YOU safer, it makes your friends safer. Bring them along and you'll all be more likely to ski another day.