There are tools out there you can pay for to do this work for, things like linkdetox.com can be helpful to identify the bad links. Something like Rmoov is great to then begin to removal process.
If doing it on your own, you'll need to check out each questionable domain manually. You can rule out big domains that you know are not spammy, and focus on the ones you have no idea about. When looking at a domain, ask yourself the following:
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Is this site indexed in Google?
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Could I easily create a followed link from this domain to mine? OR pay for one?
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Does this site seem to be scraping information of mine from other sources?
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Is this site in English (or whichever language your site is in)?
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Is it a crappy directory site? Article submission site? Other easily exploitable kind of site?
These are the sorts of things to look out for. Google doesn't want to count links for you if you made them for SEO purposes, or paid someone else to. If you look at a site, and it appears that their business model is building links, or they are spammy in anyway, you know it's a red flag.
Also, I'm learning more and more that when you're on the fence about a domain, disavow it.