In its basic form, a corporation is a type of 'privileged democracy'.
Instead of every citizen having a vote, votes are allocated on the basis of share ownership. In the most basic form, each share you own gives you 1 vote. In most public companies, very few shareholders vote [because their vote is statistically meaningless, and they have no particular insight into what they want in their Board]. This means that often the Board is voted in by a "plurality" [ie: 10%-50%] of shareholders who are actually large institutions (like investment firms or pension funds which own many shares of the company).
Now, what do shareholders actually "vote on"? You vote to elect individuals to be members of the Board of Directors ("BoD"). The BoD is basically an overarching committee that theoretically steers the company in whatever way they feel best represents the shareholders (because if they do not represent the shareholders, they will get voted out at the next shareholder meeting). The Board members are typically senior individuals with experience in either that industry or a relevant one (ie: someone who was a top lawyer may sit on the BoD and be a member of some type of 'legal issues committee'). These positions typically pay some amount of money, but often they are seen as a form of high prestige for someone nearing / after retirement. It is not typically a full time job. It will typically pay far, far less than the role of CEO at the same company.
The BoD meets periodically, to discuss issues regarding the health of the company. Their responsibility is to act in the interests of the shareholders, but they themselves do not necessarily own shares in the company. Often the BoD is broken up into several committees, such as an investment committee [which reviews and approves large scale projects], a finance committee [which reviews and approves large financial decisions, such as how to get funding], an audit committee [which reviews the results of financial statements alongside the external accountants who audit them], etc.
But arguably the main role of the BoD is to hire the Chief Executive Officer and possibly other high level individuals [typically referred to as the C-Suite executives, ie Chief Financial Officer, Chief Operating Officer, etc.] The CEO is the Big Cheese, who then typically has authority to rule everyone below him/her. Typically there are things that the Big Cheese cannot do without approval from the board, like start huge investment projects requiring a lot of spending.
So the Shareholders own the company [and are therefore entitled to receive all the dividends from profits the company earns] and elects members of the Board of Directors, the BoD oversees the company on the Shareholders' behalf, and the CEO acts based on the wishes of the BoD which hires him/her.
So how do you get to be a member of the Board, or the CEO? You become a superstar in your industry, and go through a similar process as getting any other job. You network, you make contacts, you apply, you defend yourself in interviews.
The shareholders will elect a Board who acts in their interests. And the Board will hire a CEO that they feel can carry out those interests. If you hold a majority of the shares in a company, you could elect enough Board members that you could control the BoD, and you could then be guaranteed to be hired as the CEO. If you own, say, 10% of the shares you will likely be able to elect a few people to the Board, but maybe not enough to be hired by the Board as the CEO.
Short of owning a huge amount of a company, therefore, share ownership will not get you any closer to being the CEO.