Adding a modifier is non-destructive — the mesh underneath is untouched. Applying one bakes it in permanently, and the order in the stack matters.
Steps
Select the object and open the Modifier Properties tab — the wrench icon in the properties editor.
Add Modifier, then pick from the menu: Subdivision Surface, Mirror, Array, Solidify.
Adjust it live. Nothing is committed yet, and you can turn it off with the icons in the modifier header to compare.
To bake it in: click the dropdown at the right of the modifier panel and choose Apply, or hover over the modifier and press Ctrl+A.
Applying works top-down. A modifier cannot be applied while one above it is unapplied, so apply in order or move it to the top first.
Worth knowing
You must be in Object Mode to apply — in Edit Mode the option is greyed out, which is the most common reason it seems missing. Applying a Mirror before you have finished modelling means mirroring by hand from then on, so leave it until last. Objects with shape keys refuse to apply most modifiers at all.
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