This will vary depending on the search engine, and the age and structure of a website. There are elements that can speed this process up, however, search engine optimisation needs to be approached as a long-term investment in your business.
For faster traffic, you may want to consider pay-per-click services.
With Google and Bing, a website can be listed in a short period of time. However, high rankings can take anywhere from four to six months. Less competitive keywords can take less time, highly competitive keywords, can take longer. With all the algorithm updates Google made in 2013, it has become extremely important for digital marketing specialists and webmasters to take a more careful and serious approach to SEO. As a result, effective SEO is not about getting fast results, but long term results that are as 'Google future proof' as possible.
Note: Be careful of unethical companies that promise fast listings with high rankings on keywords for your website. In many cases, tactics used are frowned upon by reputable companies, and more importantly, the main Search Engines. So while you may achieve high search engine listings quickly, once the search engines find out they have been "duped" then your risk your website being banned altogether, which could see your site drop from Google for six months plus.
The goal is to provide a long-term sustainable - and honest - approach to building your listings.