Rather than taking a knife it to trim the ends off, all you need to do is bend each spear gently between your fingers until it snaps. There's a natural breaking point which will remove all the woody stem to leave you with only the tender vegetable.
As you can see from the photos and video below, this point can vary a lot between different stems, even from the same crop of asparagus, and it's hard to second-guess it by appearance. But by taking advantage of the natural breaking characteristics, you can make sure you don't get woody bits stuck between your teeth, without wasting any of the good stuff.
PS I did this deliberately slowly for the video, but in reality it's much faster.