Indoubt wrote:

I have scanned my competitor's website with SEO SpyGlass, see a pile of links, now what do I do next?

You try to get links to your site from the same locations, and the way to do that depends on what kind of site that is - be it a forum post, a blog article a directory article or a banner ad.
Indoubt wrote:

I'd like to know what links give my competitor the most traffic, how I do this?

As said above, there is no fast answer to that, but you could try comparing Alexa ranks of the backlink locations - Alexa rank deals with traffic and can be related to that.