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Most of the time you can tell from the charge. Like F- Cl- OH- etc are all monodentates. SO42- is bidentate etc. Ethylenediammine is a bidentate cause there are 2 nitrogens each with one lone pair. So looking at the number of nitrogens can be a good indication of the number of bonds it can form.
You can figure out by drawing a complete Lewis structure, but since that takes a while--especially for something like diethylenetriamine (it makes three bonds, so it's tridentate), it's better just to memorize the chart of ligands he gave us.