Your first line:
#/usr/bin/perl
Should be:
#!/usr/bin/perl
This is an operating system thing, not a perl thing, and won't affect you if you are using a Windows system or calling the script from the command line (e.g. "perl myscript.pl")

open(DATA, "data.txt") or die "error opening file $!";
@data = <DATA>;
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if ($data =~ /$word/) {
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forget this, i was talking crap.

Nuance

Baldrick, you wouldn't see a subtle plan if it painted itself purple and danced naked on top of a harpsichord, singing "Subtle plans are here again!"

use warnings;
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In this case I think your problem is that you're double-chomping $word. When reading input you only need to chomp once to remove the line terminator (CR/LF).

print "Search for what: ";
chomp(my $search = <STDIN>);
@words = split(/ /, $search);
open(DATA, "data.txt") or die "error opening file $!";
@data = <DATA>;
foreach $data(@data) {
  foreach $word(@words) {
    if ($data =~ /$word/) {
      print $data;
    }
  }
}
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Double chomping doesn't hurt anything. Yeah, its a waste of cycles, but chomp only removes white space characters. Double choping on the other hand would be bad (unless that was what you wanted to do)

@data = <DATA>; does not read only one line. it reads all available lines from the DATA filehandle. has everybody gone mad?

in scalar context, the <FH> operator returns a single line, but in list context, it returns them all. '@data =' is clearly a list context.

#!/usr/bin/perl -w

use strict;
open(TEST,'test.pl');
my @test = <TEST>;
my $line_number = 0;
foreach (@test) {
    ++$line_number;
    print "$line_number: $_";
}
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#!/usr/bin/perl 


print "Search for what: ";
chomp(my $search = <STDIN>);
@words = split(/ /, $search);

open(DATA, "books.txt") or die "error opening file $!";

while (<DATA>) {
$matches=0;
    foreach $word(@words) {
         
        chomp($word);        
        if (/$word/i) {
            print unless ($matches > 0);    
                        $matches++;                
        }
    }
}
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-- zdog (Zenon Zabinski)
   Go Bells!!

One thing to note: The regex in your foreach loop has to be compiled several times (potentially) for every line, which can be a performance drain. A better approach is to precompile your regexes using the qr// operator (described in perlop).

#!/usr/bin/perl 

print "Search for what: ";
chomp(my $search = <STDIN>);
@words = split(/ /, $search);

# Turn words into regular expressions
@words = map {qr/$_/i} @words;

# If you don't want the user to have to
# worry about regex syntax, use this instead:
# @words = map {qr/\Q$_/i} @words

open(DATA, "books.txt") or die "error opening file $!";

while (<DATA>) {
        $matches=0;
        foreach $word(@words) {
                if ($_ =~ $word) {
                        print unless ($matches > 0);    
                        $matches++;                     
                }
        }
}
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#!/usr/bin/perl 

use warnings;
print "Search for what: ";
chomp(my $search = <STDIN>);
@words = split(/ /, $search);
open(DATA, "books.txt") or die "error opening file $!";

while (<DATA>) {
    foreach $word(@words) {
        chomp($word);        
        if (/$word/i) {
            print;        
        }
    }
}
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But now how would I get it to only print out the entry once even when there are multiple matches

-- zdog (Zenon Zabinski)
   Go Bells!!

But now how would I get it to only print out the entry once even when there are multiple matches
Like so:

#!/usr/bin/perl 

   use warnings;
   print "Search for what: ";
   chomp(my $search = <STDIN>);
   my %found;  #used as a set later
   @words = split(/ /, $search);
   open(DATA, "books.txt") or die "error opening file $!";

   while (<DATA>) {
           foreach $word(@words) {
                   chomp($word);           
                   if (/$word/i) {
            print unless defined($found{lc($word)}); 
            $found{lc($word)}=1; #indicates that word has been found
                                 
                   }
           }
   }
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Update: This prints the line for each word only once. If you instead want to print each line only once, regardless of how many words it matches, try this:

#!/usr/bin/perl 

      use warnings;
      print "Search for what: ";
      chomp(my $search = <STDIN>);
      @words = split(/ /, $search);
      open(DATA, "books.txt") or die "error opening file $!";

      while (<DATA>) {
              foreach $word(@words) {
                      chomp($word);           
                      if (/$word/i) {
                           print;
                           last; #skips checking this line against oth
+er words         
                      }
              }
      }
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I would use a hash, like this:

if (/$word/i) {
    print unless (++$matches{$word} > 1)    
}
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I suppose you could use $_ in place of $word if you wanted.

Update: After seeing swiftone's post I realize that I forgot to adjust case. Thanks swiftone.

if (/$word/i) {
    print unless (++$matches{lc $word} > 1)    
}
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UPDATE: I stand corrected.
As always, I continue to learn daily. Thanks.

Actually,  @data = <DATA>; will normally slurp in the whole file.

A filehandle read called in a list context populates the whole file into the list, one line per element.