This is an attempt to go moderately deep on a particular happiness topic. For a broader overview of the topic I highly recommend Sonja Lyubomirsky's The How of Happiness and lukeprog's How to Be Happy. The Wiley Blackwell Handbook of Positive Psychological Interventions has a fairly in-depth treatment of this topic and others.

I'm going over three different forms of gratitude exercises, what the data says about them, and my personal experiences with them.

Gratitude Journaling/Listing

The act of recording several items you are grateful periodically, generally once a day or once a week. Here's another exhortation for the practice.

Data

Per Davis et al 2016, gratitude lists are by far the most commonly studied gratitude intervention (to such an overwhelming degree that I'm going to pretend the meta-analyses just look at this).  The same study suggests that gratitude is effective at improving psychological well-being, with suggestive trends not reaching significance for improving measures of anxiety and gratitude when compared to measurement only control groups. Gratitude interventions appear to have a larger impact on psychological well-being than gratitude! Using alternative activity control groups keeps the benefit to psychological well being, and now there is a significant improvement in anxiety. I would take this with a grain of salt, as several of the alternative activities seem plausibly anxiety increasing (hassle lists are a common alternative activity).

Cregg & Chevvens 2020 look at the results restricted to impact on depression. They come away with an effect size of 0.29 at post test and 0.23 at follow up. This is nominally quite small, but should be compared against Ciprani et al's analysis suggesting antidepressants have an effect size of around 0.3 (SSC had a good discussion on this). When framed this way, encouraging gratitude as an antidepressant exercise seems like a no-brainer.

Anecdata

I've kept a daily gratitude journal consistently for around 3 years, I started beeminding it more recently. In its best case, journaling helps me re-live the parts of the day that were the most fun and realize the good that I have even on quite poor days (some rough food poisoning during a trip to Hyderabad comes to mind). It is 'very' easy for this to turn into a chore, however. My partner found this activity extremely chorelike and unpleasant, and eventually quit it.

My best advice for keeping the right frame of mind is the next activity, prayer. Taking a moment to try to genuinely express your thankfulness in your heart is great for getting in the mindest. 

Prayer

In the context of gratitude, I'm talking about prayer that is directed outward and expressing thankfulness for specific things in your life or the world at large. Requestive prayer (asking for a particular outcome), meditative prayer, and ritual prayer (repeating prayers from a book or scripture) seem best examined separately.

Data

One study finds improved results from reframing gratitude journaling as prayer, but its source is a theological school. There are several suggestive correlational studies (1, 2, 3). This seems a comparatively little studied intervention by 'serious academics', and could use some more love considering the cheapness of the intervention and the promising correlations.

Anecdata

Despite being a long time atheist, I highly recommend this. I expect plenty of folks to find this distasteful DoubleThink, but you needn't actually believe or even pretend to. Address your thankfulness to Jonas Salk, Scott Alexander, or Jeff Bezos as you please.

I've also noticed that the happiness/kindness giants in my life have a strong habit of faith and prayer. Obviously many of the faithful I know are not happiness buddhas, but the three happiest people I've met all routinely pray. It's a good call to copy them until I find a better idea.

Public thanking

I'm mushing together gratitude visits and otherwise directly thanking an individual.

Data

Gratitude visits show large short term benefits to happiness that fade over approximately 6 months. I was unable to find studies on making a habit out of gratitude visits, to see if the benefits could be sustained.

Anecdata

This feels great from both sides of the equation. I have never felt more valued in my job than when one of my senior peers sent out an email thanking me for adding more tests to our system. Similarly, I genuinely teared up when composing an email thanking a colleague for their support as I integrated with their system. Merely remembering these experiences is a significant support of happiness. Thank people! Especially at work, it makes both of you look better and feel better.

I haven't done a formal gratitude visit (and doing so now is hard because of the pandemic) sadly, nor have I heard directly from folks who have.