[regex] How to replace a string in an existing file in Perl?

I want to replace word "blue" to "red" in all text files named as 1_classification.dat, 2_classification.dat and so on. I want to edit the same file so I tried this code but it does not work. Where am I going wrong?

@files=glob("*_classification.dat");
foreach my $file (@files)
{
    open(IN,$file) or die $!;
    <IN>;
    while(<IN>)
    {
       $_='~s/blue/red/g';
       print IN $file;
    }

   close(IN)
}

It can be done using a single line:

perl -pi.back -e 's/oldString/newString/g;' inputFileName

Pay attention that oldString is processed as a Regular Expression.
In case the string contains any of {}[]()^$.|*+? (The special characters for Regular Expression syntax) make sure to escape them unless you want it to be processed as a regular expression.
Escaping it is done by \, so \[.

$_='~s/blue/red/g';

Uh, what??

Just

s/blue/red/g;

or, if you insist on using a variable (which is not necessary when using $_, but I just want to show the right syntax):

$_ =~ s/blue/red/g;

None of the existing answers here has provided a complete example of how to do this from within a script (not a one-liner). Here is what I did:

rename($file, $file.'.bak');
open(IN, '<'.$file.'.bak') or die $!;
open(OUT, '>'.$file) or die $!;
while(<IN>)
{
    $_ =~ s/blue/red/g;
    print OUT $_;
}
close(IN);
close(OUT);