How to do a link building analysys?

I'm not sure about that I'll say is about "link building analysis", but maybe this will help. It is not quite black hat style but probably could be useful.
1. Look for backlink profile in majestic or ahrefs of your clients site.
2. These backlinks might be blog or forum posts, twitter or facebook links and many more.
3. Sources of these links in some way can describe your site niche. Each of them has its own characteristics like PR, DA etc.
4. Then find sites similar to them by topics and characteristics.
5. Try to figure out how much does it cost (money, time etc) to publish on these sites . And how much traffic they can derive.

And the same thing about competitors. But first find nearest competitors in serp (semrush or serpstat can help here).
Try not to stand out from your competitors, just be little better.