What causes tongue pain on one side?

Trauma or ulcers... Most common causes or unilateral pain "on" the tongue are trauma from burn, bites, cuts, or dentistry, or ulcer--aphthous, or herpetic. Most commonly it is one sided.
See an Oral Surgeon. It could be a numer of things: apthous ulcer, inflammatory disease like lichen planus or migratory glossitis, B12 deficiency, or a tumor. It's best to have it evaluated.