You're much better off grabbing either strawberry-perl-5.30.0.1-32bit-portable.zip or strawberry-perl-5.30.0.1-64bit-portable.zip from http://strawberryperl.com/releases.html.
(I can't give you the full link because I can't actually access http://strawberryperl.com/releases.html at the moment.)
I believe that the more common choice is for the 64bit version.

Then you just unzip the package to your choice of location, cd to that location, execute portableshell.bat .... and start running whatever perl commands you like.
Strawberry Perl ships with latest Time::Piece so you won't even have to install it. (But even if you did have to inatall it, it's as simple as cpan -i Time::Piece)

To answer your question:
1) tar zxvf Time-Piece-1.33.tar.gz
2) cd Time-Piece-1.33
3) perl Makefile.PL
4) nmake test
5) nmake install

You'll need a Microsoft C compiler, and also nmake (which will probably ship with the package that contains the C compiler).

You may need that Microsoft Compiler to be VS 6.0, as that's the compiler that built your perl 5.8.6. (OTOH, other more recent versions of Microsoft compilers might suffice.)
If you run cl you can see the version of the compiler that you have. For VS 6.0, it will be 12.00.something:

C:\>cl
Microsoft (R) 32-bit C/C++ Standard Compiler Version 12.00.8168 for 80
+x86
Copyright (C) Microsoft Corp 1984-1998. All rights reserved.

usage: cl [ option... ] filename... [ /link linkoption... ]
[download]

Cheers,
Rob