Craft or obtain Eyes of Ender
Hold an Eye of Ender and use it
Follow the direction the Eye travels
Pick up the Eye if it drops back down
Repeat from different spots to triangulate the stronghold
Keep moving toward where the Eyes consistently lead
Use more Eyes as needed to confirm the location
When an Eye starts moving downward instead of forward, dig in that area
Search underground for the stronghold entrance
Explore the stronghold corridors once found