The easiest way is to use the record function available directly on the page Upload recording but it is an experimental function : depending on browser and operating system, you may have some clics or have level compression. So better record with another method for the moment.
You may record directly to your computer combined to a measurement mic, using the record function on page “Upload my record”.
On a computer, there are some free softwares to play and record simultaneously : ie Audacity has an overdub function (in preferences) : https://audacity.fr/
You can also use a portable recorder (Zoom or others) or your mobile phone with a usb mic : ie Iphone and Umik connected with a lightning-usb adapter.
Using a mobile phone, it is recommended to compare to measurements done another way to be sure than the recording feature of your phone does’nt reduce frequency response.
Record in uncompressed format .wav mono, 16bits or 24 bits, 44.1 or 48kHz (aiff or flac will be accepted later).
In all case be sure to avoid any process on the played sound file and on the recording : no EQ, compressor, limiter, filter,…