What you will need depends on the outputs available on your turntable and your stereo receiver.
Line-level output
If you have line-level output, you could record that with the aid of a USB "sound card" and an application to record sound input. I'm guessing that this is what your receiver provides on its external recording jack.
Phono-level output
Many higher-end turntables produce phono-level output instead of line-level output. This needs to be run through a pre-amplifier to adjust the level and to re-adjust the relative volumes of various frequencies according to the RIAA equalization curve. Receivers with phono inputs typically have built-in pre-amplifiers – and it is also possible to buy separate pre-amplifiers that just convert phono-level output to-line level output.
Once you've converted this to an analog line-level signal, see above.
USB or USB-C output
Some turntables can digitize audio themselves for the benefit of a computer. You can think of these turntables as having built-in USB "sound cards". You may still need an application on the computer to capture the digital audio.