Wait for the temperature to rise, and stir occasionally to ensure the sugar dissolves
As the temperature gets close to boiling, begin stirring more often and don't walk away.
Bring slowly to a boil over the low heat
Once the syrup hits a boil, turn off the heat
Allow to cool to room temperature before storing
A "rich" variety of simple syrup is to double the sugar amount but keep the water the same. If measuring by volume this becomes a 1:2 ratio of water to sugar. Rich simple syrup makes cakes and jams sweeter with less moisture being added to the recipe.
All simple syrups, except for the rich variety, if you are using US Imperial measurements are a one-to-one ratio of sugar-to-water. One cup of water to one cup of granulated sugar.
For metric measurements, ratio is 4:3, or 75% of granulated sugar to whatever measure of water you use. For example, 400 ml of water to 300 g of sugar.
But here's a trick: if you are using regular old granulated sugar, the stuff you would put in your coffee or tea or sprinkle over your cornflakes in the morning, then you can just measure the sugar and water by volume as a 1:1 ratio, that is, 400 ml of water to 400 ml of granulated sugar, or 1 cup of water to 1 cup of granulated sugar. This trick only works if you are using granulated sugar. The finer baker's sugar, or brown sugars with larger crystals should always be done by weight.
This recipe is incredibly forgiving, a little over in one ingredient, a little under in another ingredient. It doesn't matter.
Before putting the simple syrup in to a container for storage, be sure to let it absolutely cool to room temperature first. The last thing you want is to pour molten sugar over your hand, or have a glass bottle shatter due to thermal shock when you pour in hot molten sugar.
Stores in the refrigerator in a bottle with a tight fitting screw-cap almost indefinitely.