The easy way is to use Google search console to find all 404 pages and fix them. To find the list of all 404 pages, you can log in to the Google search console account and click on Coverage.
You check out the error box (with red colour). If there are any 404 pages their details will be shown underneath the details bar .
If you see any links from an external domain which is broken due to misspelling or you might have changed something, you can notify the owner to fix the link or set up a 301 redirection on your blog to redirect that link to original link.
Desktop tool call Integrity for Mac can be used to find broken links
Depending upon your blog size, this may be a lengthy process, but in the long-term, this is going to be useful for your readers and most importantly for the search engine; though this trick will not tell you about the broken external links from your blog. You should consider using other tools like the broken link checker plugin or Sitebulb to find such links as well.
Do let us know how you take care of 404 pages and broken links on your blog. Do you use the Google search console or other third party tools?