Assuming that you know the table name, and want the names of the data columns you can use the listed code will do it in a simple and elegant way to my taste:
import sqlite3
def get_col_names():
#this works beautifully given that you know the table name
conn = sqlite3.connect("t.db")
c = conn.cursor()
c.execute("select * from tablename")
return [member[0] for member in c.description]