When you click Browse, the Apply Design Template dialog box opens to the default location for templates (.pot files). If you're after a .ppt or .pps file, browse to the folder it's saved in.
All you do is select the file you want and click Apply; the design is applied to your presentation.
Only the design is applied
When you apply a design template through Browse, only the slide's styles (fonts, background, colors, bullets, layout) are applied; none of its content. And that should be your goal in using Browse: you want a slide's design only.
Note If the file you apply contains multiple design templates, the first template is applied to your file, and you're prompted with a message asking if you want the rest of the templates added to the presentation. These don't automatically apply to any slides; they just become available in the task pane.