You shouldn't be thinking about "taking effect", but rather the individual stages.
For example, Google has to find the link by crawling the page. Popular sites are crawled more often than unpopular sites, and popular pages are crawled more often than unpopular pages.
The Forbes.com home page is crawled much more regularly than something like
www.myrandomblog/articles/meaningoflife/references/article.html
Once crawled, it has to be indexed. The page will only be indexed if it meets quality standards.
You also have to consider that pages linking to the page also have to be indexed. A new page by itself has very little power to pass on. As soon as other pages are crawled that link to the page that links to your site, the page that links to your site is given more authority. But it is only when the page is recrawled again that the authority is passed to your site.
In other words:
Google needs to find the page that links to you. That could take minutes if the page is known, and on a popular site, or weeks if buried in an unpopular blog.
Google then needs to index that page. Nothing will happen if it doesn't do this.
Google then needs to crawl many other pages that link to the page that links to your site. Again, that might take minutes if the pages are popular, or weeks.
Google then needs to recrawl the page that links to you.
This is why the answers in this post are so variable. A good quality, established site that has traffic to it (PBN or not) is likely to be crawled more regularly than a new web 2.0. Build links on high quality sites, and they will pass power to you much faster than links from sites less regularly crawled.