Connect the color-coded (normally red and white) RCA cable ends to the turntable and then, also, to the inputs at the back of the receiver. If your turntable is already connected to your stereo receiver (likely if you normally listen to your LPs), you can skip this first step. If that same RCA cable has a third wire included with a U-shaped connector (the grounding wire), connect it to the grounding screws on both the receiver and the turntable.
Grab the stereo mini-jack cable. Find the main or auxiliary outputs at the back of the turntable and plug in the other two RCA-like (again, normally white and red) plugs. Then, plug the black, small mini-jack into the audio input of your computer. Make sure everything is plugged in and properly connected before continuing on to the next step.
Search online for free software. This should result in a variety of options. For extra features and more professional options, buy impressive audio recording software that can run you upwards of $1,000. But to start, look for free software such as Audacity (which works for both PC and Mac and is relatively simple to use) to get the job done. Download the software of your choice, install it, and open it up. Find the incoming signal preferences and make sure you select 16-bit stereo .wav or .aif audio file. Choose the sampling rate 44.1 kHz. Doing this will save you time and energy later on, when you get to the CD burning stage.
Clean the vinyl record you are about to record and set it on the turntable. Hit record on the audio recording software and press play on the turntable (which, of course, in old vinyl-speak means lift the needle yourself and lay it ever so gently on the record). Let your record play all the way through. You'll be able to clip the recording into individual tracks/songs after you're finished. Once it's done, stop recording. You now have the raw material, ready to burn.
Cut/clip the recording into tracks/songs if you so desire. Also, if you're interested in noise reduction to get rid of blips or scratchy/hissing vinyl noises, open your noise reduction software (mentioned as "optional" in the list of necessary components) and make the changes you feel necessary. Many enjoy the natural, old-fashioned tones and scratches of a vinyl record and like to leave the recording as is.
Open your CD burning software (most computers come with CD-burning software these days, and most media players such as Windows Media Player for PCs and iTunes for Macs include this feature) and compile a list of the tracks you want to burn onto the CD. Insert the blank CD-R or CD-RW into the writeable disc drive and press burn. You've done it. Now, for the next vinyl record, repeat steps 4 to 6.