Question

Do you have any tips on reading electronic component datasheets?

Answer

Read the whole datasheet. For a device like an op-amp or transistor this is not onerous. For a microcontroller it is. For a microcontroller you need to familiarize yourself with each function and review the details of functions that you are using.

Terminology There is industry standard terminology that has evolved for electronic components. It is important to understand the definitions. Sometimes the definitions are in the datasheet, sometimes there is a separate guide and sometimes you need a textbook.
Absolute Maximum Ratings Understand the limitations of the component. Absolute maximum ratings are ratings beyond which component damage can occur. It is important to not exceed these conditions.
Specification Conditions Although the terminology is standard the specific test conditions for each specification are not. It is important to account for these differences when (1) determining the proper component and (2) when comparing devices. If your application deviates from the specified conditions (operating voltage, operating temperature, etc) you may need to look into the datasheet graphs to determine the specifications for your application.
Application Notes Most datasheets have a variety of application circuits. These may consist of just the peripheral circuitry to demonstrate a particular feature or could be a complete design. These can provide an excellent starting point for your design.
Reference Designs A reference design is one of the most valuable application notes that a manufacturer provides. A good reference design will demonstrate the proper application of a component and the proper circuit layout to achieve the specified performance.
Component Package Specifications Review the component packages and the recommended PCB land patterns. Although there are industry standard packages (SOT23, SOIC, PQFP, etc) the pin spacing can vary, the recommended pad geometry could be different and the package size could be different. The dimension tolerances may differ between manufacturers.