The first and most important thing about being an employee is following directions. The reason this is the most important part about being the best employee is because bosses don't like to tell people more than once to do something or how to do it, so if you can follow direction and learn the job inside and out very quickly you will be a true asset to the company.
The second thing that will make you the best employee is that you go above and beyond what people ask you to do, which is ideally what all bosses want. The great thing about doing more than is asked is that your boss will see you as more valuable than other employees and therefore you will make more money and secure your job for years to come. Going above and beyond what people ask is not a tough thing to do, it just requires that you prioritize your time and duties so you can still get everything done.
And the third thing that will make you the best employee is contributing to the growth and profitability of a business. The reason bosses and even owners love employees like this is because they know if they have more than just managers and executives looking after the growth and profitability of a business then the business is actually going places. Finding great employees is something that doesn't happen much and therefore employers hold on to great employees as long as they can and usually that means that you will have more power to demand a raise in which you will now make money fast. Just think, if you can be a great employee then you will have a lot of room to talk about raises, extra days off, and even more benefits, so all in all being the best employee you can be is in your benefit as well.