Answer:
Not a whole lot. Mexico was going through a civil war at the time, and the belligerents of World War I, while fighting all over the world, did not have fronts that were close to Mexico (Germany’s navy in the Pacific once passed more or less close to the Mexican coast, but didn’t actually stop by or anything). Mexico would play a relatively important role in the war with the episode of the Zimmermann Telegram, however.
In January of 1917, German foreign secretary Arthur Zimmermann sent a telegram to the Mexican government proposing a military alliance, where Germany would supply Mexico with weapons and materiel so that Mexico could invade the United States and recover territories such as Texas and New Mexico. The British intercepted the telegram and published it, which incensed the American public and was a major impetus in the United States declaring war on Germany in April of 1917.
(As for the proposal itself, the only country that could supply Mexico the weapons to take on the United States was the United States itself, so even if the Mexican government had been agreeable to the proposal it wouldn’t have worked out.)
Although Mexico’s northern neighbor (and its southern neighbor Guatemala) would declare war on Germany and the Central Powers, Mexico still considered Germany a friendly nation and stayed neutral in the war despite outside pressure. Mexico would go on to join the allies and deploy combat troops during World War II, but that is out of the scope of this question.