Fundamental analysis is the practice of evaluating a company's stock price by comparing base elements in the company's balance sheets as well as general market factors. It does not include chart analysis, which is the domain of technical analysis.
The main principle of fundamental analysis is to find profitable companies to invest in by comparing revenues, sales, management, etc. There are two types of drivers to look at in fundamental analysis: internal drivers and external drivers. Internal drivers are company specific (e.g. revenue, net income, assets, debts, etc.). External drivers are things that can affect the company's profitability but is not company specific (e.g. the economy, industry averages, etc.).
The analysis of internal drivers can be broken down into two components: balance sheet numbers/valuations (you can calculate); and, news/management/analyst ratings/economic outlook (you cannot calculate). The items you cannot apply numbers to like news, management style, etc., are subjective so discussion of these factors with others will help.
With balance sheet numbers and valuation techniques you can get a general appraisal of whether the company is overvalued or undervalued. This can be done in many different ways. The most common is in the form of a P/E ratio.
The analysis of external drivers is more subjective, as it requires a broad knowledge and, discussion of future industry growth, politics, economy, etc. These influences are important but cannot be easily calculated.