The hypoglossal nerve is usually tested by asking the patient to stick out their tongue, and move it from side to side. Even at rest, with a chonric lesion half of the tongue will be wasted, and the other half will point towards the normal side (away from the lesion) due to the presence of resting tone in those muscles; this was demonstrated in Question 21.2 from the first paper of 2014. Acute lesions may present with fasciculations.
The "central" supranuclear lesions tend to cause mild and transient weakness, because the hypoglossal nerve nuclei receive bilateral cortical input. Hemispheric lesions rarely cause a clinically important CN XII palsy.
Nuclear lesions are frequently bilateral: there is little space in the medulla, and the nuclei are close together.
Generally, anything that causes a peripheral spinal accessory nerve lesion will also cause a hypoglossal nerve lesion. The nerve can be compressed in the hypoglossal canal or the jugular foramen.
The LITFL summary of cranial nerve lesions is without peer in terms of useful information density.
Walker, H. Kenneth, W. Dallas Hall, and J. Willis Hurst. "Clinical methods." 3rd edition.(1990). Chapter 65. Cranial Nerve XII: The Hypoglossal Nerve - by Kenneth Walker