The first one you said is that the computer receives signals, which is very convenient and does not require additional equipment. You only need to extract the signal from the mixer RECOUT or AUX (if not), and make the extracted signal line into a three-core interface to access the MIC port of the computer.
The second connection is the same as above, that is, after the signal is led out, you need to find a recording device, such as a recording pen or a cassette, which is not necessary for you.
Recording operation: If RECOUT is connected, the position of the function key will be different according to the mixer. You need to find the RECOUT function key (some mixers don't), and when it is turned on, RECOUT will output audio signals. This method is not recommended for beginners, and it will be confusing to operate.
The other operation is simple. Suppose you receive the signal of AUX 1 2, find the knob of AUX 1 2 in the input signal supplier you want to record, and turn it on until the sound is appropriate. Each input corresponds to an AUX. If you want to record that signal, just open its corresponding AUX 1 2.