Percentage problems involve three key parts: the rate expressed as a percentage, the base quantity which is equal to 100%, and the percentage which is the part of the base. There are multiple ways to solve percent problems, including using fractions to represent the rate over 100 and multiplying it by the base, setting up a ratio and proportion between the rate over 100 and the percentage over 100 and solving for the percentage, or using the formula that the percentage is equal to the rate times the base.