Lou,
If you are just interested in the strip from the south area to T.I. and the Fashion Show Mall, I would go with walking, taxi or the #301 bus as Lee has already mentioned.
Yes, there is a strip trolley.....very slow and takes forever. You might want to check out all the information on the strip trolley by going to the TalkVegas homepage (click on at the bottom of this page), go to Las Vegas links, then to Las Vegas Convention & Visitors Authority. There you can click on visitor information and then transportation. It will tell you all about the strip trolley's schedule, where it runs and costs. Just be aware the cost may be slightly higher than stated. They will even show you a picture of the strip trolley.
In addition:
There is a monorail from MGM to Ballys.
There is a monorail from Excalibur to Mandalay Bay with a stop on the return at Luxor.
There is a monorail connecting Monte Carlo with Bellagio.
There is a tram from Mirage to T.I.
These monorails and trams are all free.
Plus, there are free shuttles to most of the local casinos on the outskirts of the strip.
You may find that, once you have your itinerary planned, you can combine many of the above without using the #301 bus or use it very little.
If you have any questions concerning the above, don't hesitate to ask.
Beth