That "Browse..." dialog you see in many programs is the Microsoft Common Dialog Control. To add this into your project, go to Project -> Components (CTRL+T) and scroll down to Microsoft Common Dialog Control.
You can also create a Common Dialog Control without adding the component into your project, however this seems to fail on about half of users' computers.
This code can load a listbox from a file (line by line), or save a listbox to a file (line by line).
I have written both ways and put them into two separate modules.