Alright. I think I have come to a decision. Now what do I do, or, shall I say, HOW DO I physically handle it. I'm by myself, and I really dont have anyone to help me. I hate this....
Oh, I am so, so, sorry. I hate this for you too




There are several ways to do this and it has been discussed a lot here on BYC. Each of us have found what "works" for us.
You want quick and least amount of pain for the chicken, plus something that you can do yourself if a vet is not an option.
Personally, I use cervical dislocation or the broomstick method. I am not trying to be graphic, but a hen is easier than a rooster, just because of the size of the chicken - you will need more strength. I will tell you, it can be unsettling the first time, there will be some flapping around, this is normal reflex reaction. It is also normal for a little bit of liquid/saliva to come from the beak after death, that is just coming from the crop.
The best video I've found that shows this method is the one that @aart found - it's in post#29 of this thread https://www.backyardchickens.com/threads/broomstick-method-question.1187027/page-3#post-18746119
Now...there are plenty of other methods out there - some severe the jugular or cut the head off.
https://www.backyardchickens.com/threads/euthanasia-information.1195265/
I cannot tell you how sorry I am for you. There is no easy way to do this. I usually talk to them, have a cry, then get a mindset of why this has to be done - sick/injured, declining health, they are in pain and suffering - then set to the business at hand.