It is obviously an individual belief. If one is OK with (or even if your not) with folks being grateful to G!d, or Allah, or Krishna, or whichever deity we should (IMO) accept folks non belief or gratefulness to the universe, chance,.gravity, or whatever.
I mainly want to understand how they do it or how it processes in their mind or what it means.
When people say Allah or God or whatever, many are thinking of different things, and when non-believers talk of these things, they also are often seeming to think of sort of Zeusy image type cartoony figures that they expect others might subscribe to which they don't.
For me though, I can describe in detail that what I am grateful to is some kind of responsible force for bringing about anything in the macro sense and immediate micro sense down the line as well as immediately, one great mechanism that I view as hyper conscious like my mind multiplied and encompassing all information and consciousness. Its something I can talk to and which in some way is expected to register what is said even as it is thought to have produced it in the first, the One Big Me that I'm a small part of. Its also the same thing that whispers stuff to me I shouldn't know or be able to predict, which give it a "super" impression of having some sort of extra ability which I don't consciously have or control (at least in no way knowingly).
When people are sick, in the middle of nowhere, with no one around, and they scream "Please Help Me!" they are typically talking to this thing, this great big ever-presence or imaginary atmosphere that seems to be the go to in emergency freak out type desperate reactions. That thing, even without any sophisticated theology or reasoning behind it or name edits, seems to be a widely known and understood feeling and idea, even without an image or face or gender, the great Call Line when a person says "Help!" or "Thank You!" in the middle of nowhere to apparently Nothing. That is everyone's natural and first God, it seems, before much brainwashing, and is similar to our own thoughts or mind that we might also talk to, but seems also to be external to us or our heads even though our heads and thoughts are all we ever really deal with directly.
I think even Atheists might deal with that thing or that impression sometimes, or at least in language, before sometimes snapping themselves out of it and remembering that God can only ever mean a stupid cartoon that stupid people subscribe to, and that nothing hears their cries or responds to them, that out in the middle of nowhere, there is no help, and that people are expected to have died out in the middle of nowhere even as they called out and pleaded for help like a dying insect on their back, and simply starved to death, remaining as open mouthed skeletons crying out to what wasn't even there to hear or help them. Why be grateful and how shall we do it? No matter what is given credit, its terrible failures to do whatever everyone ever wants it to do might be enough to make us likewise turn away from speaking to it as a disciplined protest (and how stupid is it to protest against something that isn't even there to care).
So how does one practice Godless gratitude, and why should they once the technique is described? Probably because it makes one feel good or better to think on the good things and be pleased about them. In that case, it likewise makes some people feel good to think or do many strange or unreasonable things, and so long as they don't threaten us or step on our toes as to invoke War, they should simply do whatever at all makes them happy? However untrue, unrealistic, or personally dangerous?
Well regardless of what we might think, that seems to actively be the case as it is now.
The world of mankind is Libertarian and Libertine even as it obstructs itself with its obstructing checks and balances.
Some people talk about being grateful, and they mean to be grateful to what they say is nothing, but just doing it, even to pray, again to nothing though. It boggles my very simplistic mind which requires the forms to be filled or else an error comes up and I can't complete the registration.
Are the people who believe in nothing "to" be grateful towards excluded from gratefulness, or are they secretly talking to God?
s/dogs/etc. are beneficial to people recovering from heart attacks/open heart surgeries as well as other major surgeries, even speeding up the recovery time iirc.) 
