As it says in the help document gave by ArMoraer. The command creates the file for you if it not exist and if you have rights to write in your work directory.
Another explanation of your error may come from the queries that ask to display everything (*) in the 'table_name'. But I assume you know a bit of SQL and python if you are asking this question. (No offence, just saying).
Anyway, after creating the Database you need to initialize the database with the geometry table and co. So, this is my suggestion, first, check where you are working and if you don't have rights to write on that directory change it
# Check where is your working directory
os.getcwd() # gives the path where you are working on
# change directory
Then you can create your database
# importing pyspatialite
from pyspatialite import dbapi2 as db
# creating/connecting the test_db
conn = db.connect('test_db.sqlite')
# creating a Cursor
cur = conn.cursor()
# initializing Spatial MetaData
# using v.2.4.0 this will automatically create
# GEOMETRY_COLUMNS and SPATIAL_REF_SYS
sql = 'SELECT InitSpatialMetadata()'
# creating a POINT table
sql = 'CREATE TABLE test_pt ('
sql += 'id INTEGER NOT NULL PRIMARY KEY,'
sql += 'name TEXT NOT NULL)'
# Test the table
sql = 'select * from test_pt'
It should work, if not try to reinstall your pyspatialite libs.