To find the TextElement on the page layout use the ListLayoutElement() with a filter of TEXT_ELEMENT for the type to return.
import arcpy
from arcpy import mapping
mxd = mapping.MapDocument("CURRENT")
textElem = mapping.ListLayoutElements(mxd, "TEXT_ELEMENT")
Now a list of all TextElements are returned. The next step is to find the text element you want to change. Each TextElement has a property called 'name' and when you perform your cartographic duties, I strongly suggest you set this. It makes it easy to update the elements.
import arcpy
from arcpy import mapping
mxd = mapping.MapDocument("CURRENT")
textElem = mapping.ListLayoutElements(mxd, "TEXT_ELEMENT")
for elem in textElem:
if elem.name == "txtTitle":
elem.text = "Mr. Toads Wild Ride"
elif elem.name == "txtCurrentDate":
# make an element have dynamic text of current date
elem.text = """<dyn format="short" type="date">"""
mxd.save()
del mxd
Now you might be thinking dynamic text, what the heck is that!?!? well it's exactly what it means, it's dynamic, it changes, and it's awesome. You can check out more here.