This process goes on until either all the sugar is gone or the yeast can no longer tolerate the alcoholic percentage of the beverage. Different yeasts produce different results, and have different tolerance levels. Yeast can't live on sugar alone. It is happiest when it has a real organic soup of acids and nutrients and minerals, like any other living thing. Bacteria also like oxygen, so while it is good to agitate the solution before yeast gets added so the yeast can be fruitful and multiply, it is best to keep as little oxygen from getting to your beverage after fermentation has started.
Honey has a lot of what yeast needs, but is somewhat resistant to being fermented by itself.
A pure honey solution will ferment, but it can take three months to a year to ferment. Yeast nutrient and some sort of acid added will speed this up greatly, taking more like a month to ferment, depending on the concentration of honey in solution. Fruit juices often have all that yeast needs all by themselves. Notably grape juice is a favorite, as it has the acids and tannins and sugars needed. Apple juice stands on its own quite well too.