iPhone UITableView. How do turn on the single letter alphabetical list like the Music App?

Supply your own index characters:

- (NSArray *)sectionIndexTitlesForTableView:(UITableView *)tableView {
    return[NSArray arrayWithObjects:@"a", @"e", @"i", @"m", @"p", nil];
}

and then:

- (NSInteger)tableView:(UITableView *)tableView sectionForSectionIndexTitle:(NSString
    *)title atIndex:(NSInteger)index {
        return <yourSectionIndexForTheSectionForSectionIndexTitle >;
}

You will need sections.