There are a few ways. A USB turntable ($) or an older analog turntable. If you use the analog, you'll either need an older receiver or an adapter for it. You'll also need an audio adpater to go from RCA plugs to a mini-plug. Then you need audio recording software. You can buy it, or find one free. I use Audacity, which is free and can be easily found on the web.
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Well, vinyl records are still being made, so as long as you're willing to pay enough for it someone could certainly cut a CD into vinyl. It would require some fairly specific equipment though.
There are several methods available to transfer vinyl records to CD. A standard turntable and preamp connected to a turntable can be used, but it is much simpler to use a USB turntable to transfer the record to a digital format on a computer. Once the record has been digitized it is a simple matter to burn the digitized files to a CD using CD burning software.