While it can be spelt a variety of ways, agreement after that can be difficult.It is a business to some, and understandably, they extol their own theories.
However, search engine optimisation doesn't have to be complicated beyond reach of average site owner.
Its essence is to simply make your page as spider friendly as possible, and having keyword, search phrases, density somewhere close to accepted requirements of search engines.
Too high a density may be considered "spamming", and is dependent to some degree on particular engine in question. The correct density is one that will satisfy such an engine that keywords, phrases, are repeated often enough not to be incidental. Logically, word "false teeth" which is now within body text of this article should not cause a search engine to believe that is what it is about. Remember, we are not dealing with a human editor, and relevance must be established with software, less sympathetic to context, in its English meaning, as we are.
Search engines can have different algorithms or indexing criteria.
S.E.O. must change as indexing criteria changes, so what is good today, may have to be re-considered tomorrow.
The view of many is to make site/page easy to navigate, with respect to internal and external links. Java script can present a problem for some engines, and should perhaps be kept to a minimum. Some people will tell you that raw HTML is simpler to "read", spider-wise. Sure, it might be simpler, but javascript rich pages are indexed none less.
For anyone to guarantee that they can get you to number one, is a little optimistic, as everyone cannot practically or theoretically achieve such a goal.
Surely, anywhere on first page of matches would not be a bad thing. All of us don't necessarily opt for number one match, and those with any research experience will "skim" through descriptions, to go some way in deciding best match. Descriptions, should you be favoured by an engine, may tip balance towards you.
Of course, this approach doesn't represent all surfers, so variables will always exist.
To achieve number one for a spurious or unusual term/word/phrase is relatively easy, and no great boast. Like wise, for less unusual terms or keywords for rare products or less competitive markets.
Little or no search engine optimisation experience should be needed in such cases.
It is almost certainly true to say that any advantage in case of competitive keywords/markets, is really where benefits of search engine optimisation come into play.
It is also true to say that where searches are confined/focused or country specific, task is somewhat easier than if search was "web-wide". For example, if your product was rubber tyres and you only delivered within your own country, then web results will have a less commercial benefit to you.
Of course, another variable would be if your country produced unusually high numbers of rubber tyres, in which case search engine optimisation would need extra consideration and input.
Generally speaking though, any use of search engines may convince you that major players seem to dominate. However, it is not to say that they cannot be toppled, so to speak. From an engines' relevance viewpoint, these may or may not be "tightly themed", but often have relevance, with respect to time. This is a bid by engines to return results appropriate with time we live in. The annals of history are not foremost on minds of surfers/researchers, and therefore updated content carries some weight.