What is the best way to stop tiny ants from entering my home?
You have to stop them at the source. Use baits that ants will gather and take back to their nest, or follow the trail back to the nest and Raid the entire trail + nest.

I've also been known to put a pesticide in my lawn and flower beds once or twice a year to keep them from getting near the house. I try to make a 10' perimeter around the home.