Simple MWBC definition
A multi-wire branch circuit is one in which a single neutral wire carries return current corresponding to more than one hot wire. Under NEC rules, the hot wire(s) and corresponding neutral, if any, must be enclosed in the same cable or conduit.
Figure out whether there might be any MWBC in the panel
Look around the perimeter of the panel. There are many places where branch circuit wires come in, either as cables or as loose wires in a conduit. Look closely at each set. Any cable or conduit that contains an odd number of insulated wires may contain a MWBC. Also, any conduit that contains fewer neutral wires (white or gray) than hot wires (any color except white, gray, or green), may contain a MWBC.
Confirm whether the suspects really are MWBC
For any of those sets of wires identified above as possible MWBCs, follow each wire in the set. If two or more go to circuit breaker hot terminals (ie not the neutral terminal of a GFCI or AFCI breaker) then there's a MWBC in there. In the case of wires in conduit, it's possible that some of them are members of an MWBC while others aren't. That complex scenario is beyond the scope of this answer.
Some might argue with this method because it counts the 120/240 circuits commonly used for clothes dryers and ranges as MWBC. I'm not entirely certain whether NEC considers them to be MWBC or not, but from a practical standpoint it's somewhat irrelevant: like MWBC, these circuits also need to land on a handle-tied circuit breaker. (They also require the breaker be common-trip, whereas for basic MWBC common-trip is optional, but that's whole other ball of wax.)