That answer depends on the inputs, infrastructure, permissions, and the starting point.
First of all you need to assess if this question is because:
1) You have a client and he/she wants to know how long will it take and if they can have a guarantee about it, or
2) You have your own website and you're seeing how long will it take for you to achieve what you want
Any high profile company or a startup SEO expert will say: IT DEPENDS... it is the same as asking, how long does it take for the flu to be cured?.. it depends on your immune system, stress levels, if you want to take a medical treatment or if you want to be cured with time alone... it all depends.
SEO depends in many factors like:
a) Definite goals: A concrete measurement of what you want to achieve and the time needed for that
a1) Industry and Competition: There are industry niches that are less competitive than others... most of them need to be evaluated before starting. There are things that your competitors are doing that are completely wrong so you need to identify those and get ahead.
a2) Current website state: to see quick impact you need to start evaluating the homepage and main pages, many sites have been "punished" because they used erroneous strategies that are buried there, so you need to build your success on solid bases.
b) Web architecture: If the site you are managing can be modified for meta-tags or tags and if you are making changes to try some other techniques, try to know about servers replication too--this will help in managing expectations. If you have a client and they have a global corporate site, the modifications or adjustments can be slow since there are rules and policies to be followed, and a simple change can affect their eCommerce, sales, customer service pages or many other things that not so many Managers know about. If you have your own website for example in Wordpress, you need to take into account what can you modify and how to do it on a periodical basis without breaking anything.
c) Content, concept and keyword relevance: Google Hummingbird and Panda changes for instance, are centered now in concept search not keyword search so you need to be relevant for the SEO to have a quick effect
d) Web design: This facilitates the keyword /concept relevance, Quality Score, CTR, and the bounce rate, but above all the client's interest.
Hope this helps, you need to evaluate a lot before saying an approximate time frame since SEO depends on many things.