Nancy, I've never used (someone on this site was using them for small birdbaths or feeders) but they sell a threaded flange at most hardware/home improvement stores. It's a circular piece of metal with holes around the outer edge and it's got a threaded coupling in the center. I think it was cast pipe and they use to spray paint with Rustoleum before embedding in their piece. Hope this helps. Billie

What Billie is talking about is a floor flange. they sell them at most hardware stores and the big box stores.
You can thread an adapter into it which will allow you to go from thread to slip so you can use your copper pipe.
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Thanks Billie and Bonecarver. I have seen the floor flanges, and I"ll keep that in mind for larger pieces. I'll keep looking for ideas for smaller pieces.

Here is another option I have used in the past to attach copper tubing to the back of a leaf to make a leaf birdbath stand up.

Go to the plumbing department of a home improvement store of your choice or even a local hardware store. Look around for the copper tubing you are wanting to use for the stand and then look for the following fitting that will mate with the size of copper tubing you are using.

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As I was making the tufa leaf casting, I just embedded the fitting into the back of the leaf casting and piled the tufa mixture up around the fitting. The following picture shows the fitting in the mixture after staining the backside of the leaf

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Once all is dry and cured, just insert the copper tubing into the fitting and stick the leaf in the garden amongst the flowers.

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Closeup of leaf
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Thanks! I'll keep that in mind for my larger pieces! The photos are great, by the way!