1. Keep good boundaries. Everyone has an imaginary monkey on his/her back and many people want to get rid of theirs. If you are convenient, then the other person may try to throw theirs at you. The key is to throw it back at them! If you don't do this, then you are going to end up with two or more monkeys on your back! The other person might state that s/he is too busy to do the work that has been assigned. If you agree to do it for that person, you risk becoming resentful, especially if you realize afterwards that the other person has more free time that you because you are doing his/her work. (Of course, it is a different story if it is your supervisor who is asking you to do extra work because then you will need to cooperate).
2. Ensure that you have the necessary resources. It is not appropriate for an employer to ask the employee to do things unless they provide the time, materials and support that are needed to complete the task. One might need special equipment, additional training or perhaps someone to help finish the work by the scheduled deadline. Employees need be good at assessing what is needed and assertive enough to make the employer aware of what is missing. It's about thinking and acting in a professional manner.
3. Let your employer prioritize. It is easy to get caught in a situation where, as an employee, you feel that you have to decide what to do first. You might make the decision, do the work, and then find out that you are in trouble because you didn't meet the expectations of the organization. When you find that you have too much to do, it is wise to ask your supervisor or manager to make the decision about where to focus your efforts. That way, they will take responsibility and you will have direction.
Your employer is paying you to help grow their business and generate profit. You will be viewed as very valuable if you do what is needed in the most efficient and competent manner possible. This can easily be done if you keep good boundaries, ensure that you have the necessary resources and let your employer prioritize!