At present from the time an article is published, it can take as long as weeks or as little as minutes for the page to appear the in the Google search results. This does depend on the page, the site and how fresh that content needs to be. The more popular the site and the more pages it has in the index, the more likely that the Google crawlers will visit sooner.
Now, Google is working on getting content into the index even faster. They have been testing a real time index API.
From Search Engine Land:
“Google is testing a real-time indexing API. In a talk Thursday at Google I/O, Google’s Richard Gingras said the purpose is to give trusted publishers a way to send Google their content immediately, without Google having any delay in discovering that content. Google can then surface that content to searchers immediately, in real-time, without any delay.”
Something to note is that the API will only be open to trusted publishers. Although it will likely expand to a program where sites can achieve some kind of trust score to qualify. This will likely have little impact on SEO as fresh content generally applies to categories like news, reviews and current events.
It is also possible that in the long run, the majority of the index will be through this API. This could be another method of reducing webspam, and ultimately improving the quality of search results.