The original 1996 Tomb Raider and the Unfinished Business bonus levels were designed for DOS and should install and play just fine under Windows 95/98/Me. However, a bit of effort is needed to make them work with newer versions of Windows. If you've never done anything like this before, the process can seem a little intimidating, but it's really not that hard.
UPDATE: I have not had time to rewrite this entire page, but if you have the Steam or GOG version of TR1 and want a simple fix, try the Tomb Raider 1 Automated Fix - Improved Graphics, Resolution, Music + Expansion Pack by Carlmundo, posted on the Steam forums. You can then disregard all the info below.
This page used to contain step-by-step instructions but lately I've been too busy to keep it up-to-date. I will try to rewrite it at some point, but for now, I offer the following list of links which should help in your quest to install these classic games.
For questions or issues related to Glidos, as well as an overview of its features, visit Glidos.net.
For questions or issues related to the Tomb Raider 1 Advanced Installer, as well as an overview of its features, please visit this page on Tombraiderhub.com.
Additional support is available on the following sites:
For help running the original Tomb Raider and Unfinished Business on newer Macintosh operating systems, please visit MacRaider.
ACKNOWLEDGEMENTS: Glidos was created by Paul Gardiner. His site includes additional credits for the help he received in its development. Many thanks to Paul for the tireless help he's given the gaming community. The Tomb Raider 1 Advanced Installer was created by Gidierre. It incorporates the OpenSource DOS emulator DOSBox.
Stella's Tomb Raider Site: tombraiders.net.