I don't know that it's a new year's resolution, because those are so trite and usually get broken immediately. Also, I didn't start it on January 1st; it was probably closer to December 30. All I know is that this a priority of mine right now: I want to change to become a more grateful person.
Gratitude requires a certain framework of beliefs; the two I can think of off the top of my head are the need to (1) acknowledge the existence of the giver and (2) acknowledge that the gift wasn't deserved. Before you can be grateful for anything, you have to realize that there's a giver. This is easy with things like Christmas presents; they usually come with a tag on the present. (Hint: The tag gives you two options, and you're better off picking the one that isn't your name.) Sometimes the giver is anonymous, like in a Secret Santa exchange, but it's obvious that the gift came from a giver nonetheless.
Many people miss out on opportunities to be grateful because they don't realize there's a giver. Things like beautiful days, oxygen, and friendly cats don't come with a tag saying they're from God, but He's ultimately the source of all of them. If you don't believe the God of the Bible exists, or if you believe there's a god out there but he's not involved in human affairs (unlike the God of the Bible), then you see all these things as random events, and there's no way for you to be thankful for them. You can be happy for them, and excited about them, and appreciate them, but you can't be thankful.
The other requirement, as I see it, is for you to acknowledge your unworthiness, to admit you don't deserve the thing received. When you deserve something, it's not a gift - if you work 10 hours for your boss, you expect to receive a paycheck, and if you don't get it you're going to court (if you live in Minnesota, give me a call!) Gratitude only comes if you don't deserve the thing you receive. It's going to be tough for you to be grateful if you have a high estimation of yourself, because in your mind you don't receive many gifts. If you take the perspective, though, that you're nothing without God, that it's by His grace alone that you live, breathe, and exist on this earth, then suddenly everything becomes a gift.
For years now, I've believed that God exists, but I haven't had a very realistic perception of what I deserved. I was thankful for extraordinary gifts here and there, but they were few and far between. As a result of that mindset, I quickly ran out of things to be thankful for, and had the luxury to begin counting all the things I didn't have. To be entirely truthful, there are a lot of things I don't have. Right now, I don't have a job, I don't have millions of dollars, I don't have fame, and on and on and on. There are legitimately a lot of things I could have but don't.
As soon as I changed my perspective, though, and thought of myself as not deserving anything, I found myself overwhelmed with blessings - it's as if I was buried under a mound of gifts so deep that I couldn't see beyond them to the gifts I didn't have. It was sparked by a conversation with a friend about being thankful for (forgive me) bowel movements. This friend had undergone several surgeries just to be able to engage in this basic, primal function, and there were days when the endeavor was painful for him beyond words. However, the whole experience has made him immensely grateful for something 99% of the population takes for granted every single day.
When I realized that I wasn't even entitled to the basics, everything started opening up for me; the presents rained down. I can eat, see, hear, talk, and breathe on my own - I know people who can't. Think how happy an African woman who walks 5 miles a day to fetch water would be to have any car; I should be happier than that every single day for the car I have, instead of groaning about how it got scratched up in an accident recently. I don't deserve it; I don't deserve any of the blessings in my life, but that's why I can also be exceedingly happy for them. Think of all the happiness I've been missing out on by assuming that things came to me by chance, and by assuming that I deserved them. Just changing my perspective on those two little things has been giving me so much joy lately, and I hope you can experience it too.