You are likely to get a lot of answers to a question like this, so you might find it easier to do a search for "humane culling" and read the results on previous (very long) threads.
While it's harder for you, the easiest thing for your chicken is beheading or cervical dislocation.
With cervical dislocation, you can hold your bird under your left arm, possibly with a towel, hold her by the shoulders, and then pull her head quickly out and up with a twist. This breaks her neck. You have to do it pretty hard to get it right the first time with a full grown hen.
Beheading with a hatchet or something is surer for a first-timer.
Some will recommend co2 or freezing. I don't recommend either of these since they are much slower ways to die. They are easier on the human, but i can't believe they're easier on the chicken.
I'm so sorry for your loss. Many many of us have been there, and we know what you're going through.
If you're burying her, i find it's much easier to dig the hole ahead of time, so that after she's gone, you can immediate bury her and not have to deal with her body any longer than necessary.
Again, i'm very sorry.