Is there any chance you could post a picture or two of the lamp? (Perhaps one showing the whole lamp and another with a close-up of business end of the light.)

Lamp parts for fixtures using ordinary light bulbs are easy to buy and quite inexpensive.

Although I've converted quite a few antique lamps from kerosene to electric, I've never reworked a halogen lamp. Still, I might be able to help if I knew more about what you're working with.

What's challenging about this question is that it has more to do with aesthetics and design than with the mechanics of swapping in an "Edison socket" to use ordinary bulbs or CFLs.

I'd guess that that's why replies have been slow in this thread.

I'm not sure why you'd want to change from halogen, whilst not as efficient as a cfl they put out a lot more light than a conventional bulb and it's a much nicer looking light. If I had my druthers, my whole house would be halogen.

Sorry , I can't post pictures. As for the lamp it is solid brass and it was expensive so I don't want to just throw it away. Details are: has a 'eye w/ off on switch' in the middle of the pole. Bought a new 'light' but it still won't work. (halogen ,,I have been told get very hot) so I'm trying to convert it. Has electric to the off/on switch but not to bulb. I'm thinking the 'eye' isn't working?? Knowing nothing about this is the problem. Lamps are easy to rewire so I'm thinking that if I just pull all the wires and do a total would be best. Thought I could save the eye and off/on switch but will have to check into that.
I know I could take it in and have it done but I'd like to save $$ on that. Anymore ideas will be welcomed.
Thanks

Is there an integrated transformer in the thing? A lot of halogen bulbs are low voltage....I'm not sure what you mean by the 'eye' but if power goes to the switch and not beyond, it'll be a simple break in the wire or bad splice, or a faulty lampholder. Lampholders for most halogen fittings are considered consumables and will need to be replaced now and then, they are usually ceramic and tough but with the heat generated they can fail. If you take the lamp to a lighting store they can probably help you diagnose the problem and sell you the fitting if required. I can't imagine what sort of lamp it is, but I'd really recommend sticking with the halogen than just reworking it, it's a much nicer light.