The safest place is on the piste - avalanches across pistes do occasionally occur but they are extremely rare and, wherever you're skiing, the local pisteurs will have done a lot of work to make and keep the marked, open runs safe. Do not enter closed runs - they're closed for a reason; usually for your safety.
If you do fancy the off-piste...
Know the Avalanche Risk Levels - from 1 (Low) to 5 (Extreme) - covered on J2Ski here Avalanche Risk Scale.
Key Point: Level 3 is Considerable, not "average" or "medium" and certainly not "OK". Around half of all skier-triggered avalanches (and fatalities) occur on Level 3 days.
Read the local Avalanche Bulletin - before you leave the pistes.
Take Safety Kit - take, and know how to use, the essential equipment: a Transceiver, a Shovel and a Probe at a minimum. Airbags are a sensible addition. If you don't understand the need for these, you will not be safe and you will endanger others. Seriously.
Learning More
Here's an earlier post on J2Ski "We need to talk about ... Avalanches!" that links to some excellent Youtube resources and includes a video on "persistent weak layers" - which is directly relevant to the current situation across much of the Alps right now.
Check out and follow Henry's Avalanche Talk / Blog at henrysavalanchetalk.com/hat_blog/.
Read the info at European Avalanche Warning Services