Step 1: Follow the salivary wiring. Parasympathetic fibres for the submandibular gland leave the superior salivatory nucleus, run with the facial nerve, and branch off as the chorda tympani.
Step 2: The chorda tympani then piggybacks onto the lingual nerve. The submandibular ganglion is suspended from the lingual nerve, and its postganglionic fibres pass straight into the gland, so clinically the lingual nerve is the relevant supply.
Step 3: Distinguish the parotid pathway, which uses glossopharyngeal fibres through the otic ganglion and is delivered by the auriculotemporal nerve. The inferior alveolar nerve is purely for the mandibular teeth and gingiva.
Step 4: Hence the nerve associated with the submandibular gland is the lingual nerve.\[\boxed{Lingual\ nerve}\]