This is kind of a wide-open question with a million potential answers.

If you have a trusted travel agent, that could be the easiest (in terms of minimizing decisions and searching on your part). But you'll still have to hand over the same information as you would booking it by yourself and it probably won't be absolute cheapest.

If you search and book it yourself, it all depends on the complexity of whatever itinerary you want to book. For multi-carrier ones I've typically found flights with ITA or Kayak and booked them via orbitz. For specific-carrier flights I usually use the carrier's website.