Vitamin D improves gut flora.

Be slim and fit.
Be social.

Eat less (calorie restriction), especially less protein.

Have pets:

Shown by a study of people and animals in Africa.

Exercise:

Shown by a study of mice.
Shown by a study of 37 breast cancer survivors.
Exercise may work via lactate.

Glyphosate (Roundup herbicide) caution.
NSAID pain reliever caution.

Get sufficient quality sleep
Avoid artificial (high-intensity) sweeteners

Shown by two studies of mice.

Consume a variety of live cultured (fermented) foods

Probiotic Lactobacillus rhamnosus GG ATCC helped 12 healthy individuals, 65 to 80 years old. But most probiotics are useless.

Consume a whole-food, unprocessed, varied, plant-based (vegan) diet.

Diet rapidly and reproducibly alters the human gut microbiome. The animal-based diet increased the abundance of bile-tolerant microorganisms (Alistipes, Bilophila, and Bacteroides) and decreased the levels of Firmicutes that metabolize dietary plant polysaccharides (Roseburia, Eubacterium rectale, and Ruminococcus bromii). A plant-based diet led to a decrease in the pathobionts such as the Enterobacteriaceae and an increase in commensurable (protective) microbes such as Bacteroides fragilis and Clostridium species belonging to clusters XIVa and IV, resulting in reduced intestinal lipocalin-2 and short-chain fatty acids levels.
The Mediterranean diet is close.
The change in gut microbes works fast.
Less ammonia in the stool - fiber-rich resistant starches to the rescue.
Consume inulin (defined) and oligofructose (defined).
Consume resistant starch, such as beans, which is prebiotic.
Less pathogenic bugs in the gut.

Beans mean less putrefactive bacteria in the gut.

Include oatmeal and other whole (best intact) grains and coffee - prebiotics.
A plant-based diet supplies dietary (better than supplemental) fiber, and complex carbs. Human alimentary enzymes are not able to digest most complex carbohydrates and plant polysaccharides. Instead, these polysaccharides are metabolized by microbes which generate short-chain fatty acids (SCFAs), including acetate, propionate, and butyrate. Dietary fiber can only be broken down and fermented by enzymes from microbiota living in the colon. Short chain fatty acids (SCFA) are released as a result of fermentation. This lowers the pH of the colon, which in turn determines the type of microbiota present that would survive in this acidic environment. The lower pH limits the growth of some harmful bacteria like Clostridium difficile.

Dietary fiber is what nourishes good gut bugs.
Eat like a rural African.
Especially important for the elderly.

Include dietary polyphenols - colored fruits and veggies, tea, and cocoa.

Cranberries are an excellent source of polyphenols.
A bit of (polyphenol-rich) red wine might help,

Consume adequate protein, to supply nitrogen.

A whole-food plant-based diet is more effective than probiotics.
Eat asparagus- a prebiotic.

In any case, one should avoid the western diet. Mice on a western diet also had less diverse gut fungi. High dietary intake of animal products, processed foods, alcohol and sugar, support a gut microbiome that encourages inflammation, while a diet rich in plant-based foods was found to promote gut microbial communities that have the opposite effect.