How can I prepend http to a url if it doesn't begin with http?

Python do have builtin functions to treat that correctly, like

p = urlparse.urlparse(my_url, 'http')
netloc = p.netloc or p.path
path = p.path if p.netloc else ''
if not netloc.startswith('www.'):
    netloc = 'www.' + netloc

p = urlparse.ParseResult('http', netloc, path, *p[3:])
print(p.geturl())

If you want to remove (or add) the www part, you have to edit the .netloc field of the resulting object before calling .geturl().

Because ParseResult is a namedtuple, you cannot edit it in-place, but have to create a new object.

PS:

For Python3, it should be urllib.parse.urlparse

I found it easy to detect the protocol with regex and then append it if missing:

import re
def formaturl(url):
    if not re.match('(?:http|ftp|https)://', url):
        return 'http://{}'.format(url)
    return url

url = 'test.com'
print(formaturl(url)) # http://test.com

url = 'https://test.com'
print(formaturl(url)) # https://test.com

I hope it helps!

For the formats that you mention in your question, you can do something as simple as:

def convert(url):
    if url.startswith('http://www.'):
        return 'http://' + url[len('http://www.'):]
    if url.startswith('www.'):
        return 'http://' + url[len('www.'):]
    if not url.startswith('http://'):
        return 'http://' + url
    return url

But please note that there are probably other formats that you are not anticipating. In addition, keep in mind that the output URL (according to your definitions) will not necessarily be a valid one (i.e., the DNS will not be able to translate it into a valid IP address).