Depending on which button you want, it will appear if you write code in any of the OnDrilldown, OnLookup or OnAssistEdit events of the textbox. To browse for a file, you use codeunit 412 - Common Dialog Management. Set the SourceExpr property of the textbox to a textvariable and fill the variable with the return value of the codeunit's OpenFile function.
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and the textvariable will stay with the path to the browsed file, right?