Can anyone give me some pointers on replacing the engine pulley on my craftsman riding lawn mower which is about 11 yrs. Old. The bolt in the center of the pulley needs to be removed to replace the pulley but the entire pulley turns when I try to loosen the bolt. Any suggestions?

Turns every time. There are two tools I find useful. Vise grips and a pipe wrench. Applied at the proper point and leveraged against something usually prevents rotation. Without a pic it's hard to suggest something.

I would not recommend a pipe wrench or vise grips here, you could do more damage.

What you need is some good penetrating oil. Time. And an impact wrench. Then you still have to remove the pulley itself after getting the bolt out. This is where it will be a challenge. I have had to cut off a pulley due to it being "frozen" onto the pto shaft. You can use heat, but you really need a lot of guidance when using heat, because you can ruin the main seal on the bottom side of the engine.

Penetrating oil (I use Kroil) and more penetrating Oil. If it doesn't come off after a respectable rap, you could try heat or a pulley puller

Heating the pulleys will also heat the oil seal on the bottom of the engine. If you do so and ruin the oil seal, you will be disconnecting everything from the engine, and removing the entire engine, removing the oil, pulling the sump pan (oil pan so to speak), then removing the seal. Then replacing the seal, replacing the sump gasket, reinstall the sump pan, re install the engine, reconnect all connections, then start the engine. Wow, a lot of unnecessary work for using a little heat huh?
And I like "PB BLASTER" for penetrating.