Add about 1-inch of water to a medium pot (just below height of steamer basket).
Bring water to a boil over medium-high heat. Insert a steamer basket (legs of basket should be propped up if it has collapsable legs).
Set eggs on steamer basket, cover with lid right away (leave pot set on medium-high heat).
Let cook 6 - 15 minutes to desired doneness*. Runny yolks take 6 - 8 minutes, nearly set yolks are about 9 - 11 minutes, and fully cooked through yolks take about 13 - 15 minutes (hard boiled type).
While eggs are cooking fill a medium bowl with ice and water.
Once eggs are done cooking immediately transfer to ice water to cool so eggs don't continue to cook. Let rest for at least a few minutes before peeling, to chill eggs through if preferred let rest at least 15 minutes.
To peel the eggs easily crack all over then roll on countertop. Run under cold water and peel. Rinse away any debris of shells.
Store fully cooked through steamed eggs in the fridge an an airtight container for up to 1 week.
Times vary slightly based on altitude, egg size, temperature of eggs to begin, pan size and so forth.
You may find it helpful when making steamed eggs the first few times to cook an extra egg (and quickly cut open and test for doneness) until you get to know the exact time you prefer.
You should be able to steam up to about 8 eggs in a medium pot in a single layer. A larger pot can be used to cook more, cook times just increase by a few minutes.