Sich von jemandem etwas geben lassen
is a generic way in German to express that two parties agree on an exchange. It doesn't sound very fluid when literally translated into English, maybe something like "let someone give you something".
Er ließ sich vom Kellner einen Tisch anweisen.
means guest and waiter both agreed on the assignment of a table by the waiter to the guest. It may include negotiations about which table exactly and also the act of the waiter leading the guest to the table.
Ihm hat der Kellner einen Tisch angewiesen.
expresses the same outcome, but is somewhat more direct in tone, may imply that the waiter was less cooperative and just ordered the guest to a certain table, one the waiter deemed fit, possibly with less inclination to serve the guest's request. Like, for instance, the seat number on a flight which, if not payed for, is just assigned.
Note that this is not a hard rule and needs mor context, but it can be used as a way to express an interaction in different shades.