There are several ways:

use strict;

#
# first
#

my $var1="fie";    # note closing "
my $var2="fum";

my $newvariable="fee $var1 fo $var2";
print "$newvariable\n";

#
# second
#

my $newvariable2= join ' ', 'fee',  $var1, 'fo', $var2;
print "$newvariable2\n";

#
# third
#

my $newvariable3= <<EOT;
fee $var1 fo $var2
EOT

print "$newvariable3\n";

#
# fourth
#

my $newvariable4=  'fee ' . $var1 . ' fo ' . $var2;
print "$newvariable4\n";

#
# fifth
#

my $newvariable5=  'fee  fo ';
substr($newvariable5, 8, 0) = $var2;
substr($newvariable5, 4, 0) = $var1;
print "$newvariable5\n";

#
# sixth
#

my $newvariable6 =  pack 'A4A3A4A3', 'fee ', $var1,  ' fo ', $var2;
print "$newvariable6\n";
[download]

see perldoc perlop about interpolation in Quote-and-Quote-like-Operators and concatenation operator .

also please don't forget to use strict; in begin of your scripts

and, imho, the good style is to use single quotes not double quotes for string literals which are not supposed to be interpolated.