At first I tried to read through them individually and delete only those that were obviously spam, but that quickly became tedious and I just deleted the whole lot, real comments and all. This happened a few more times before I finally wised up and installed some spam filters on my site.
If you use a major blogging platform, like Wordpress or Blogger, there are some spam blockers already in place. You can tweak these to further block spam messages. At the very least you want to block comments that contain multiple links. I also use a Capcha code on my comments. It's a bit of a pain for legitimate commenters, but it does cut down on the spam.
There are more in depth spam blocking add-ons available, some free and some carrying a small fee. Research these and ensure they work well before trying them out. You will still likely lose some genuine comments, and some spam will still work its way through, but it will be much less severe than running your site with no blocking.
Finally, don't publish your email address directly on your site. Spammers regularly crawl sites and collect email addresses so they can attack your inbox. You can prevent this by either using a contact form for readers to email you, or by writing your email address out as “my email [at] provider [dot] com. It isn't perfect but it does cut down on some of the spammage!