The shareholders can also sack the board, I believe. Votes of no-confidence do happen.
If you are an owner, you will always get the right to vote (as mentioned, assuming you have voting/ordinary shares).
If you own through a brokerage, the brokerage deals with making sure voting materials are distributed to the holder. The brokerage holds those shares in trust on your behalf (and in your agreement with the brokerage, they can make money by lending your shares for short sale and so on).
If you go and look at the price of a smaller company, you will see the price zig-zag - when there is not enough 'liquidity', ie not enough shares are bought and sold to make prices change smoothly. You might put a bid in for 2000 shares at $1, but only 100 are for sale at $0.98, then the next sale is 5000 as $1.10 - you would only end up buying 100 shares. But with any large company, there are hundreds of millions of shares, often interlisted on multiple stock exchanges, and god knows how many 'limit' orders (I'll sell 500 if the price gets to $1.10! And another 500 if it gets to $1.20!).
I mostly buy and hold, but I can easily go in and go, ok, I can see the price of share X is dropping a bit... hmm, I'll put an order in to fire if the price hits Y. It's like a tug of war between the bulls (to the moon!) and bears (end of the world!) (well.. kinda :))
If you have, say, 100 shares of the Bank of America you have only a tiny amount of 'clout' with the company; but you can go to the shareholder meetings, you can ask questions of the board, and you can vote - just like in an election. Nobody can take those shares away from you, though the company can issue MORE shares which leads to 'dilution' of the value (unless they are raising money to buy something valuable, but even so your 100 shares are a smaller percentage of the whole).
The board, the directors, the managers, they are ALL your employees, and it is their job to work for the benefit of the shareholders. That is why you pay them!