Ba(OH)2(aq) + Fe(NO3)3(aq) ------->  Fe(OH)3(s) + Ba(NO3)2(aq)

I am supposed to write a net ionic equation.  I have no difficulty doing that, but first I need to make sure that a reaction will actually occur.  How can I make sure a reation will occur?

this is a reaction between 2 salts. Usually it will be a displacement reaction (beware of acids/bases in the salts). In this case we get the displacement reaction you wrote, only you need to balance it.

the ionic equation that is relevant in this case the precipitation: 3 OH(-) + Fe(3+) --> Fe(OH)3