I believe that there are two ways to do this -
1. Rebuild the entire site in Wordpress, and just let one of the pages of the rebuilt site be the Blog page. This would require the ability to select a theme that can be adapted to appear cosmetically as your original pages do.
2. Install Wordpress on the site, select a stock theme like Twenty Fourteen, add an iframe to the page where you want the blog functionality, and source that iframe with the standard Wordpress home page (i.e., blog). Use CSS to hide all of the cosmetic elements of the theme you have selected so that the page appears in the iframe without graphic enhancements.
The first alternative would be a bit more difficult than the second.
Rebuild your DW site to look more like your WordPress Theme.
Use WordPress for everything -- blog and main site.