Generally I do at after the mixer at the amp myself but the easiest way...
Your mixer has a cable that goes from the mixer to the stereo/amp. Take this cable and instead of it going to the amp it now goes to the IN on the tape deck. There will also be an OUT on the tape deck, this now goes to where the mixer used to be plugged into the stereo/amp.
Again this is the hack way of doing it, what you really want to do is find the 'TAPE OUT' or "MONITOR OUT' on the stereo/amp and connect this line to the tape deck.
totally depends on your tape deck, it may not even be possible.
That said, if it is possible:
Your mixer will have a "line out" or "rec out" RCA ouput.
Your tape deck, should have a "line in" or "rec in" RCA input.
Get yourself a good old RCA-RCA cable (male to male). Connect the inputs to the outputs.
Probably tell the tape deck to use the input signal instead of recording from the other tape deck (assuming this is a dual tape player).
There is the off chance that your input to the tape deck is not RCA but 1/8th inch (like a headphone plug). In which case you want to buy an RCA-1/8th cable (male-male) instead of an RCA-RCA (male-male).
To summarize. You need to find the output on your mixer, and the input on your tape deck. Get a cable that fits them together. Then tell the tape deck to record from that input.