This depends how precise you want to be. Downloading the entire web page wouldn't be too challenging - using wget, as Earwicker mentions above.
If you want the actual image file of the comic downloaded, you would need a bit more in your arsenal. In Python - because that's what I know best - I would imagine you'd need to use urllib to access the page, and then a regular expression to identify the correct part of the page. Therefore you will need to know the exact layout of the page and the absolute URL of the image.
For XKCD, for example, the following works:
#!/usr/bin/env python
import re, urllib
root_url = 'http://xkcd.com/'
img_url = r'http://imgs.xkcd.com/comics/'
dl_dir = '/path/to/download/directory/'
# Open the page URL and identify comic image URL
page = urllib.urlopen(root_url).read()
comic = re.match(r'%s[\w]+?\.(png|jpg)' % img_url, page)
# Generate the filename
fname = re.sub(img_url, '', comic)
# Download the image to the specified download directory
try:
image = urllib.urlretrieve(comic, '%s%s' % (dl_dir, fname))
except ContentTooShortError:
print 'Download interrupted.'
else:
print 'Download successful.'
You can then email it however you feel comfortable.