Peruse your reel-to-reel player to determine what sort of output interface it has (meaning how it gets the audio signal from the tape to an outside source, such as RCA jacks or XLR outputs.) Refer to the owner's manual of your reel-to-reel for this information or consult an expert at your local music store if you need assistance in making this determination.
Obtain an audio cable that can attach your reel-to-reel to the audio input of your computer's sound card. (For example, if your reel-to-reel player has RCA jacks for its output and your computer has an 1/8-inch jack for the input of its sound card, then you would need to find an audio cable with RCA plugs on one end and an 1/8-inch "headphone" plug on the other.) Connect your reel-to-reel player to your computer's sound card using the appropriate cable.
Download software that will allow you to convert "vinyl to MP3" (which can also be used to record and convert audio from reel-to-reel players). Use an audio conversion program like Spin It Again (PC) or Golden Records (Mac), although just about any similar shareware or freeware audio recording program will work. Follow all prompts and instructions to install the program onto your computer's hard drive.
Double-click the icon for the program on your computer (for instance Spin It Again.) Click "Record a Vinyl LP," then click "Level Wizard." Select "Analog Mix" as your recording source in the pop-up window that appears, then click "Start."
Play your reel-to-reel tape audio when prompted so that the software can measure the dynamic range of the recording for 30 seconds, after which the program will automatically stop monitoring the levels.
Rewind your reel-to-reel to the beginning of the songs that you would like to record, click "Record" in the Spin It Again program window, then start the reel-to-reel recording. Click "Stop" when you wish to end the recording.
Click the "Zoom In" button in the Spin It Again program window, then move the sliders at the beginning and end of each track to note their starting and ending points. Click "Next" to enter track information in the pop-up window that appears, then click "Next" to close the pop-up window. Click "Create Audio FIles" to save each track as a separate digital audio file or click "Burn Audio CD" and follow the prompts to insert a blank CD-R and burn the tracks to it.