If there is a single data point that is used in almost every fundamental analysis, earnings per share would be it. With that, the best way to use this is when you identify a stock or equity worth investing, find the EPS for that stock and the others that compete in the same space.
When looking for an investment, you want to find the balance between value, low risk, and reputation of the company. If you take the EPS share of the equity you are researching, be sure to look at the historical numbers as well because you want to see a trend to the upside, which means the company is becoming more profitable, fueling potential growth into the future.
As with any financial data point, it is not wise to rely on just one financial number, but rather calculating others and getting a wide and vast opinion. Also, be sure to pick apart the calculation and understand what is generating the number. Understand the net income and find out how it is projected to do into the future. Then look at dividends and see if the company is going to make more into the future. Lastly, look at the outstanding shares and see if the company has implemented a share buyback program, which will shrink the denominator. These all will factor into the number you look at and can help to tell a little bit more of the story.
If you are stuck or need more background information, head to the Internet and find ways people are using this in their research. Join an investing and trading community and ask people the most efficient ways they are using this data point. Lastly, you can reach out to an investing professional and they help you in implementing this into your analysis of equities. EPS is certainly one you should know and understand how to use because it is widely used and implemented in many valuation tools and reports.