Display first name in specific posts which contain a custom field

try get_the_author_meta( 'first_name' , 'ID')

of course, ID should be the actual user ID

@trepmal How would that work?
Changed this

function twentyten_posted_on() {
	printf( __( '<span class="%1$s">Posted on</span> %2$s <span class="meta-sep">by</span> %3$s', 'twentyten' ),
		'meta-prep meta-prep-author',
		sprintf( '<a href="%1$s" title="%2$s" rel="bookmark"><span class="entry-date">%3$s</span></a>',
			get_permalink(),
			esc_attr( get_the_time() ),
			get_the_date()
		),
		sprintf( '<span class="author vcard"><a class="url fn n" href="%1$s" title="%2$s">%3$s</a></span>',
			get_author_posts_url( get_the_author_meta( 'ID' ) ),
			sprintf( esc_attr__( 'View all posts by %s', 'twentyten' ), get_the_author() ),
			get_the_author()
		)
	);
}

to

function twentyten_posted_on() {
	printf( __( '<span class="%1$s">Posted on</span> %2$s <span class="meta-sep">by</span> %3$s', 'twentyten' ),
		'meta-prep meta-prep-author',
		sprintf( '<a href="%1$s" title="%2$s" rel="bookmark"><span class="entry-date">%3$s</span></a>',
			get_permalink(),
			esc_attr( get_the_time() ),
			get_the_date()
		),
		sprintf( '<span class="author vcard"><a class="url fn n" href="%1$s" title="%2$s">%3$s</a></span>',
			get_author_posts_url( get_the_author_meta( 'first_name' , 'ID' ) ),
			sprintf( esc_attr__( 'View all posts by %s', 'twentyten' ), get_the_author() ),
			get_the_author()
		)
	);
}

And author post url is wrong. Changes …?author=1 to …?author=0

Sorry, I think I was up too late trying to answer questions… ??

Maybe this:

function twentyten_posted_on() {
	printf( __( '<span class="%1$s">Posted on</span> %2$s <span class="meta-sep">by</span> %3$s', 'twentyten' ),
		'meta-prep meta-prep-author',
		sprintf( '<a href="%1$s" title="%2$s" rel="bookmark"><span class="entry-date">%3$s</span></a>',
			get_permalink(),
			esc_attr( get_the_time() ),
			get_the_date()
		),
		sprintf( '<span class="author vcard"><a class="url fn n" href="%1$s" title="%2$s">%3$s</a></span>',
			get_author_posts_url( get_the_author_meta( 'ID' ) ),
			sprintf( esc_attr__( 'View all posts by %s', 'twentyten' ), get_the_author() ),
			get_the_author_meta('first_name')
		)
	);
}

If that doesn’t work, my guess would be that the author-related functions aren’t getting the author ID to work with… I might find a way to pass it the id

function twentyten_posted_on( $id ) {
	printf( __( '<span class="%1$s">Posted on</span> %2$s <span class="meta-sep">by</span> %3$s', 'twentyten' ),
		'meta-prep meta-prep-author',
		sprintf( '<a href="%1$s" title="%2$s" rel="bookmark"><span class="entry-date">%3$s</span></a>',
			get_permalink(),
			esc_attr( get_the_time() ),
			get_the_date()
		),
		sprintf( '<span class="author vcard"><a class="url fn n" href="%1$s" title="%2$s">%3$s</a></span>',
			get_author_posts_url( $id ),
			sprintf( esc_attr__( 'View all posts by %s', 'twentyten' ), get_the_author() ),
			get_the_author_meta('first_name', $id)
		)
	);
}

and when the function is called,
twentyten_posted_on( get_the_author_meta( 'ID' ) );

Excellent! Managed to change the Nicename to first name(needed this function in multi-lingual posts) Thanks @trepmal