How to determine which size spoke wrench I should buy? I was advised to use a dedicated spoke wrench (not multitool) when possible, so I am looking to order one online. How can I determine which size I need before ordering it?

I do have a multitool with spoke wrenches. They are labelled 0,1,2,3. 0 does not fit. 1 fits, but it is not quite snug. Based on Wikipedia, I assume this means that I need the 3.30 mm one. Is this correct?
For the sake of making the question more general, it would be nice to also have answers explaining how to choose the right size if one does not already have such a multitool.
No this may not be correct.
The Wikipedia sizes (0, 1, 2, 3) are Park Tool specific sizes. Park Tool SW-1 is 3.30mm. Whether or not your multitool uses the same numbering as Park Tool is anyone's guess.
My understanding is that DT Swiss nipples all use 3.23mm (Park Tool SW-0, black tool). Of course your bicycle may have some other nipples than DT Swiss.
If building a wheel from scratch, I suggest choosing DT Swiss Pro Head nipples (they have a spherical seat as opposed to the cheaper but unfortunately more common conical seat), and remembering to grease the threads of the spokes well. Then the only spoke wrench size you need is 3.23mm.
To determine what spoke wrench size you need for an existing bicycle, invest in a caliper or a micrometer screw gauge.