In general, people buying and selling shares on the secondary market has no direct effect on the companies behind those shares.
However there are some indirect effects. Many companies issue new shares all the time to compensate their employees. The higher their share price tends to be, the company needs to offer fewer shares to its new employees and its existing employees have more incentive to stick around. If you have enough market clout to meaningfully affect the share price, you can potentially decrease executive pay, as many higher-level executives tend to be paid mostly in stock. On the other side of the coin, a higher share price means that a company is less likely to choose share buybacks as a way to return cash to shareholders.