I figured it out! This is what I did, pretty simple. My roadblock was just figuring out how to attach my script/component and connect it to the OnItemSelected.
using UnityEngine;
using MaterialUI;
public class MaterialCustom : MonoBehaviour {
public void OnDropdownSelect() {
MaterialDropdown dropdown = GetComponent<MaterialDropdown> ();
int currentlySelected = dropdown.currentlySelected;
string currentlySelectedName = dropdown.optionDataList.options [currentlySelected].text;
Debug.Log (currentlySelectedName);
}
}