Have a blog that's worth "liking" in the first place. Interesting, useful, entertaining, active, informative, controversial... it doesn't really matter exactly what it offers, but it's got to have something special so it's more attractive than all the other zillion blogs out there being touted by all the zillions of other bloggers, all of whom seem to think they "deserve" thousands of "likes" simply for the mere fact of existing.
Post regularly to the blog and share those posts on Facebook.
Spend a bit of money with Facebook to promote your best, most interesting blog posts.
Repeat as often as necessary.
Be patient. It may take a little while to build momentum, but if your blog is truly "likeable" you will get more followers over time.
The interesting question for me is: why do you want specifically 1,000 "likes"? What do you think this will accomplish for you?