Fundamental analysis requires a thorough assessment of a company's financial position and prospects. Based on some combination of skill and access to data, an investor should be able to derive a valuation for each potential investment with an eye toward buying stocks that are undervalued in the marketplace.
EMH assumes three things: all information is available to the market, all investors are rational and that stocks follow a random walk. The assumption about information comes in three flavors with varying measures of strength.
Under the strong form of EMH, information is universally shared and immediately reflected in share prices. In this situation, there is no distinction between private non-public information and public information, and the share price is a completely accurate reflection of the projected future cash flows of the company. In this situation, fundamental analysis is useless because the combination of perfect information and rational investors means that the stock price always reflects the intrinsic price.
Under the semi-strong form of EMH, all public information is assumed to be incorporated into the stock price almost immediately. In this case there is potential for share prices to be inaccurate or outdated because of private information that hasn't yet been shared. The implication is that there is limited potential for fundamental analysis to work when it's based on access to more accurate private information.
Under the weak form of EMH, only public market information is assumed to be incorporated into the share price. If there is breaking news about a company, weak-form EMH assumes that it is digested rapidly by the market and that the change in price accurately reflects the implications of that news. Other public and private information is not assumed to be part of the price, which implies that there is more potential for fundamental analysis to work when it's based on an information advantage.
Under all forms of EMH, investors are assumed to be perfectly rational, and the valuation of a particular stock is assumed to be accurate based on the information available. Given the same information, every analyst or investor should have the same valuation. One major strike against EMH is that some investors routinely beat the market, especially Warren Buffett.
The implication is either that some people have better information than others or that some people are better at interpreting information than others. This notion is supported by research in market movements and behavioral finance, which both show that stock prices don't always reflect economic value. While EMH remains an important hypothesis in the financial literature, it has lost traction recently.