Run a patch cable from the direct out jack of each channel to be recorded from the PA mixer to the inputs of your multitrack recorder. Typically these are 1/4-inch phone plugs in either balanced or unbalanced configuration. See the PA mixer's documentation for proper connection.
Use line inserts if direct outs are not available. Line inserts will require specially wired 1/4-inch stereo phone plugs to feed the signal to the recorder while simultaneously returning the signal to the PA.
Set input levels independently on your recorder. Direct outs and line inserts provide a signal that is after the preamp (in the case of microphones or other XLR input devices) but before the rest of the PA mixer electronics. Changes made to the PA during performance will not reflect on the signal directed to the recorder.
Connect the bus or group outputs from the PA mixer to the inputs of your recorder. Generally, you will encounter fewer buses than input channels or recording tracks. Four-bus mixers are common, eight-bus mixers less so outside of studios. Connection is usually via 1/4-inch mono phone plugs.
Arrange your PA input channels into logical groups. For example, drums may be assigned to one bus, bass to the second, guitars to the third and vocals to the fourth bus. While this gives less individual control than a direct out configuration, it offers flexibility beyond the stereo master mix.
Consider that changes to individual channels will also change in the group bus assigned. Effects can usually be routed to the master mix, bypassing the group buses so you can record the performance without added effects. This is preferable when mixing.