One way to make your blog popular is to popularise your blog on social media like Digg and Reddit. Depending on your site, you can get lots of followers and visitor. Why Google visitors specifically or are you talking about all web? Also make sure you are listed on blog directories...they are good backlinks too.
1000 visits main depends upon lot of factor, like content of your blog, useful information, blog layout, age, ranking, backlinks etc.
Having a well ranked website - you could make any article, use some social bookmarking, post some backlinks to the article on some good forums, and your article will rank awesomely. I've tried it, and it works really well. Just use Keyword Rich phrases.
Earlier I had in mind that the only way to get this is your domain have to be very old so most of your pages get indexed automatically. But after going thru each and every post in this thread, it has helped me a lot with some key factors to plan for my blog/site from the next working day. Thank you for this thread.
make sure your titles are good and catchy Use your self as a method, what type of links do you click on first when you use google? and then use that technique to improve your site...