#!/usr/bin/perl
use strict;
use warnings;

my @strings = ('A dog ate an apple',
               'A apple ate a dog',
               'A apple ate a oak',
              );
for my $string (@strings)  {
    $string =~ s/\b([Aa])(\s+[aeiou])/$1n$2/g;
    print "$string\n";
}
[download]

What would you use before the following words, though?

heir user XML yak ylem
[download]

You need pronunciation, not spelling. Update: check Text::Phonetic and related modules for that.

Update: Note failure in the case of 'an log'.

c:\@Work\Perl\monks\MadhAric>perl -wMstrict -le
"my $string = 'A log and a axe, an log and an axe';
 print qq{'$string'};
 ;;
 $string =~ s/\b([Aa])(\s+[aeiou])/$1n$2/g;
 print qq{'$string'};
"
'A log and a axe, an log and an axe'
'A log and an axe, an log and an axe'
[download]

Even ignoring the subtleties of pronunciation you pointed out, the OPed problem statement is tricky. Some cases need 'n' deleted, so I don't see how it can be done (in a single regex) without decision-making in the replacement clause, i.e., use of the  /e modifier or equivalent trick.

---

Give a man a fish:  <%-(-(-(-<

Read perlrequick, perlre,perlrecharclass

1.Read how to match a string.
2.Read How to group a matched string

my $str="a apple";
$str =~(s/a(\s+[aeiou].+)/an\1/g);
print $str
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sure vinoth, an alteration of single characters should be a character class :)

and we're on our way with the help from Basic debugging checklist

use Data::Dump qw/ dd /;
my $string = 'and a one and a two and a panda is a animal';
$string =~ (s/a (a|e|i|o|u)/an /g); 
dd( $string );
__END__
"and an ne and a two and a pandan s an nimal"
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#!/usr/bin/env perl

use strict;
use warnings;

use Lingua::EN::Inflect 'A';

while (<DATA>) {
    while ( /\b (an? \s (\w+))/gx ) {
        my ( $phrase, $word ) = ( $1, $2 );
        if ( $phrase eq A( $word )) {
            print "RIGHT: $phrase\n";
        }
        else {
            print "WRONG: $phrase\n";
        }
    }
}

__DATA__
I am a howling maniac in an hospital.
It takes a hour to win an honorable mention.
Calling him a umpire is a euphemism.
This is a united front against a evil empire.
[download]

(updated to fix a typo in the cpan link.)

One more update: a bit more logic is needed to handle various kinds and amounts of punctuation that might occur between the article and the word that follows:

while (<DATA>) {
    while ( /\b ((an?) \s\W* (\w+))/gx ) {
        my ( $phrase, $article, $word ) = ( $1, $2, $3 );
        my $bigram = "$article $word";
        if ( $bigram eq A( $word )) {
            print "RIGHT: $phrase\n";
        }
        else {
            print "WRONG: $phrase\n";
        }
    }
}

__DATA__
Suitable for a (older) child or an 'early adult'.
[download]

Here are a couple of similar approaches that differ in using a regex feature introduced in Perl version 5.10. These regexes may be a bit beyond your current regex understanding; if so, this may serve as a spur. I think the main idea to take away is of building a unit testing framework in which different approaches (to what looks like your homework) can be tried. (The original file contains other variations, but I think the ones I've shown are the best.) See Test::More and friends.