Let me give the most practical guide I can to getting cheap flights to Asia from North America, because the routes and strategies are specific.

The best value carriers for North America to Asia:

• Korean Air and Asiana via Seoul Incheon: consistently among the best value transpacific options with good service
• Japan Airlines and ANA: often competitive on sale, particularly for travel rewards redemptions
• Cathay Pacific via Hong Kong: frequently discounted and the airport is excellent for connections
• Budget carriers: Philippine Airlines, China Eastern (via Chinese cities), and Scoot/AirAsia for the final Southeast Asia leg

The open-jaw strategy: book into one city and out of another. Flying into Bangkok and out of Hanoi is often cheaper than a return ticket because you eliminate backtracking. Use Rome2Rio to sketch the overland route between your entry and exit points first.

Seasonality for transpacific: January-February (after Chinese New Year) and September-October (before Thanksgiving) are the cheapest windows. Avoid flying in late November-December, and the weeks before and after major Chinese holidays.

The budget carrier connection: fly a major carrier to Tokyo, Seoul, or Hong Kong, then switch to a budget carrier for the final leg to your Southeast Asian destination. AirAsia and Scoot have dense coverage across Southeast Asia at prices ($30-80) that US-based carriers can't touch.