ChuongPham's answer is correct, if a little dry.
So, to fix this problem you have to add the "Uses" permission to your manifest file (by default this should be "AndroidManifest.xml"), which, in XML, looks just like ChuongPham wrote, and should be inside the "manifest" tag, but not deeper (not in "application" or any other).
From Eclipse:
- Double click on AndroidManifest.xml will open a "Android Manifest Permissions" editor
- Click the "Add" button in the editor
- In the popup window choose "Uses Permission", click "OK"
- When the popup closes, in the "Android Manifest Permissions" editor a new item will appear in the "Permissions" list-box on the left (and will be selected). On the right, there is "Attributes for Uses Permission" part, which has "Name" combo-box. Select android.permission.WRITE_EXTERNAL_STORAGE in it.
- Save the manifest file and you're done. Next time you start your app, file open will succeed.