If you publish a newsletter or ezine, you should have a website geared towards getting more subscribers. This should be sole purpose of this particular website.
The first thing you should know is give your prospective subscriber plenty of opportunities to sign up. Put a sign-up form on each page of your site. Make it highly visible as well. Put it at top of each page where it cannot be missed.
You should include information on your site that will inspire return visits. It sometimes takes multiple visits to get a sign-up. Give them some reason to return to your site.
If you write articles, include them on your site. If you write an article a week, make sure that your visitor knows that you will have a new article each Monday or whatever day it will be. Try to make it a routine. People are more likely to return if they know that they will find new material on a certain day each week.
Include some type of resource page that has useful information for your visitors. Always remember that your visitor is looking for useful information. If you provide it, he is much more likely to return to your site. The more times he visits, better chance that he will subscribe.
Don't be afraid to use pop-ups on your site. Too many pop-ups can be detrimental to a site, but fact is that a good pop-up can do amazing things for amount of visitors you turn into subscribers.
Here is approach that has worked best for me. On your home page, put an exit pop-up. Offer a free ebook as an incentive to sign-up to your newsletter or ezine.
If you have an ebook that you have written, this is a great chance to get more exposer.
If you don't have one of your own, there are many that offer you opportunity to brand your own information into book. I suggest you find one of these and use it as a gift for those who sign up from your pop-up.