Turn warnings and strict both "on".

#!/usr/bin/perl -w
use strict;

my $text = "this text";
$text =~ /this/that; #### WRONG syntax #####
print $text;
#------
Bareword found where operator expected at C:\TEMP\temp1.pl line 5,
         near "/this/that"
    (Missing operator before that?)
syntax error at C:\TEMP\temp1.pl line 5, near "/this/that"
Execution of C:\TEMP\temp1.pl aborted due to compilation errors.
===============================================
#!/usr/bin/perl -w
use strict;

my $text = "this text";
$text =~ s/this/that/; #note s needed as well as '/' after "that"
print $text;

#prints: that text
[download]

Your second question:

my $text = "this text";
print $text =~ /this/;
[download]

The result of a match is True/False.  print $text =~ m/this/; is the same thing.

#match can be used like a boolean T/F
if($text =~ m/this/)
 { blah ...}
[download]

Update:

 $text =~ /this/ vs $text =~ m/this/ is a matter of style. When using the default '/' you can leave off the "m". if you use a different character to delimit the match, say  $text =~ m|this|;, then you definitely need the "m".