Ok, couldn't resist, here's some code (needs Perl version 5.10+ for \K):

c:\@Work\Perl\monks>perl -wMstrict -le
"use 5.010;
 ;;
 use Regexp::Common qw(number);
 ;;
 my @lines = (
   qq{Line 1 = 0154.45 +02 13.56 +03 64.35 \n},
   qq{Line 2 = +09 23.12 +10 8798 \n},
   );
 ;;
 my $prefix = qr{ \G (?: \A Line \s* \d+ \s* =)? \s+ }xms;
 for my $line (@lines) {
   my @numbers = $line =~ m{ $prefix \K  $RE{num}{real} }xmsg;
   printf qq{'$_'  } for @numbers;
   print '';
   }
"
'0154.45'  '+02'  '13.56'  '+03'  '64.35'
'+09'  '23.12'  '+10'  '8798'
[download]

Update: Of course,  \K isn't critical to this approach — I just like it so much... The expression
    m{ $prefix  ($RE{num}{real}) }xmsg
(\K removed, parentheses  (...) around the  $RE{...} sub-expression) produces identical output for the given input, and I'm not aware of any version incompatibilities.

See also the discussion of Regexp::Common and Regexp::Common::number in only want numerics in field.

And yes, showing some code would be good.

open(FH, "<$file");
@array = <FH>;
close FH;
open(OUT,'>','outfile.txt');
@array1 = @array[3..$#array-4];
print OUT @array1;
close OUT;
open (FILE, "/test/outfile.txt");

while (<FILE>) {

    print;

   ~ /^.*([0-9][0-9][0-9])..*([0-9][0-9][0-9][0-9])..*([0-9][0-9][0-9]
+)..*([0-9][0-9][0-9][0-9])..*([0-9][0-9][.][0-9][0-9])  .*([0-9][0-9]
+[0-9][.][0-9])  .*([0-9][0-9][.][0-9]).*([0-9][0-9][0-9][0-9])/s;


   $id = $1;
   $year4 = $2;
   $doy = $3 ;
   $time = $4;
   $speed = $5;
   $ddir = $6;
   $temp = $7;
   $baro = $8;  
   $windgust = $9;
   $gusttime = $10;
[download]

I appreciate your patience, as this is my first attempt at asking for help on this forum.

My input file follows: B A1 L+44941 C0747 *D 01+0100. 02+2014. 03+0111. 04+1820. 05+13.14 06+344.1 07+62.83 08+1017. 09+16.56 10+1811. A1 L+44951 C5311 *