Sorry about your loss...
My wife and I have had to put down dogs and cats in our family. There is a company near us that has vets that will come to your home and do this.
It's the best way to go if you must do this. Your pet doesnt go through that bit of trauma, that going to the vet can cause.
Our cat 'Blackjack' died in my arms, in our den. My Shepard 'Chief' died in his own bed. It's a better experience for you and your pet. Although it still hurts like hell...