Can I transfer music from a turntable to my computer?

Yes. If there is a headphone jack on the turntable, connect that to the line in or microphone input in your computer. Download Audacity, open it, press record in Audacity then play the record. When the record finishes, stop the recording in Audacity and export as FLAC or WAVE file. If the turntable doesn't have a headphone port, connect a microphone to your computer, place it as close as possible to the audio source, adjust the volume, do the same as above and leave the room. It is best to use a microphone with a long cable in order to be as far as possible from the computer, to avoid the fan noise being recorded. Make sure the place is quiet before starting to record.