OK. I lied. I'm not going to tell you exactly how long it takes. Truth is, there are no answers there. But, there are some guidelines and knowing how things works can put you in control of how your site gets ranked as the search engine spiders and robots crawl your site.
First, you need your site to get crawled. Search engine robots (search engine spiders are the same thing) then become aware of the content you have. But this doesn't put it in the search engines. For that, they need to create an index. Once you are in the index, your major concern is how high up you are for your keywords and key phrases. But let's start at the beginning...
Search Engine Crawl Frequency
Depending upon how popular your site is and how often you add new content, your site will be crawled more often or more aggressively by search engine robots. Since Google is the single largest, I won't bother with any others, but suffice it to say, that many of them draw results from Google or from similar methods.
To get you site crawled more often, you need to add content to it or change content. On the home page for Renegade Minds here, announcements keep the page updated every so often, and this looks good to search engine robots, and especially Google. The GoogleBot LOVES fresh content.
By being crawled more frequently, the search engines keep their picture of you up-to-date, and this improves your chances of getting into their results - your ultimate SEO goal.
Search Engine Indexes
In case you don't know what this is, a search engine index is where the results come from. Search engines can't deliver results in real time because the amount of information they have is simply too large. To make things faster, they create an index that can be quickly referenced. So, instead of taking a month or more to deliver a search result, you get that result in a fraction of a second, which most people think is a good thing =)
Search Engines Update Indexes
Google constantly updates its index, adding new entries, deleting some, and moving other around inside of the index, up or down. For example, I had a few terms that dominated the Google search engine results pages (SERPs) so massively that out of the top 100 results, I had over 90 of them and 9 of the top 10. After Google updated their index, I only had less than 50 in the top 100 results, and only about 7 in the top 10. That 2-word phrase now has 5 of the top 10 results after a couple years of reindexing.
Your job is to get your site or content into that index, and get it up as high as possible, and get it in there as quickly as possible. You really don't have much control over any of those, but with a few friendly tricks, you can exert some control.
Getting into the Index Quickly
If you're going after highly competitive terms and keywords, you're going to be out of luck unless you go over to the dark side of the SEO. A solid way to get in quickly is to come up with 5 keywords that you want to target, then go after 3 keyword phrases that combine those. Start writing content that makes sense with those and that is useful for readers.
The more content you can come up with, the better. But make sure it's YOUR content and not junk that you buy from some content provider. Google likes unique content and will reward you for your efforts. As another example, Renegade Minds ranks very well for almost anything that pertains to RealVNC, and with good reason. The RealVNC tutorials here at Renegade Minds offer real value to people, and aren't just junk pages. WRITE FOR REAL PEOPLE.
When you come up with fresh content, Google eats that up and if you've got some specific things to say to Google, you'll hit the top. At the moment, Renegade Minds rank #1 for “green manalish solo”. Being a Judas Priest fan, and with Green Manalishi being a favorite of mine (yes - it's a cover song, I know) I put out a demo of Guitar & Drum Trainer with the solo from Green Manalishi. Google regularly spiders Renegade Minds (because I always add new content every once in a while) and found it. Since it is specific, and isn't the same content as everyone else on the web has, Google puts it up at the top.
SERPs Time Frames
Ah... yes... that elusive number that you've been looking for. Real simple. If you have garbage content, don't count on anything. If you've been diligent in delivering real content for real people, and done a few smart things, it can take anywhere from a day to a few months. As a rule of thumb, a week or two is quick, but it can take you several months. There are different strategies you can use to get in quicker or up higher quicker, but don't expect immediate results in search engines - it doesn't happen like that.
For quicker SERPs results, create unique content that is specific. Take your time and make a page dedicated to 1 thing. If you can, create several pages on the same topic and spread out subtopics inside of it. Avoid terms that other well ranked pages use that you don't need.
For more competitive topics, try to get your content on other web sites with a link to your page. You won't rank well to start, but eventually you will crawl up higher in the SERPs. This can take several months.
Summary
New Content - Unique Content - Real Content
If you can come up with content that meets those 3 criterion, you will do well, or at least better than if you don't.
Cheers,
Renegade