If your blog is interested and people wish to get updates from ur blog than it will be feedburner subscribers will automatically risse
May be considered a hack since you;re changing the layout of your site but place the signup somewhere where folks will notice it. Like above the fold on every page.
Updating your blog regularly can increase your feedburner subscriber or you can tell your friends to subcribe to your feedburner or perhaps you can do some feedburner subscriber exchange
create good and quality content. Other bloggers love a site with good content they will coming back for more.