Google pagerank works by seeing how many other sites link
to you; and their pagerank effects how much influence that incoming link has on your site's pagerank.
Subdomains are treated the same as subfolders- that is
www.example.com/blog and blog.example.com get the same treatment.
In your case, creating a new domain to "promote" your site won't work. Google sees through it. For example if you have "funtimesoftware.com" and you wanted to promote it with a blog, you might make "ftsblog.com" but the thing is no matter now many links you put in the latter to the former or vice versa, it is the pagerank of those pages that matter. Basically, in order to get your pagerank up, you need actual, quality websites to link to it.
One of the most common ways to do this is to simply put your site in your signature on popular forums. In some capacity, this also encourages participation in that community; for example, if I put a link in my signature it will appear tens of thousands of times all over Computerhope, which has a rather large pagerank for search queries that are related to the content of my own site.
Spammers will often try this as well, by putting links to their site in their signatures or posts. However, since they do not truly contribute to the community and typically aim for the best return on their time investment in the manner of promoting their site as opposed to actually being there to contribute, they usually don't last long and are usually deleted right away.
I think the best way is to simply have quality content, though. Google rates the page as much on the quality of content as it does on incoming links, and as people find your pages, they might link to them on their own sites, or on other forums. For example, some of my own Blog posts have been featured or linked other sites, or linked by forum posters; the pagerank of those sites then influences mine in a positive way.
Essentially, the entire pagerank system is designed so that you
cannot do exactly what you want to do. You have to make good quality content- there simply aren't any shortcuts. The system is designed to prevent being gamed, which is actually part of why Google became so popular to begin with, since earlier search engines were easier to manipulate into thinking your content was relevant.
