System requirements
Functional:
List functional requirements for the system (Ask interviewer if stuck)...
Take original url and return a short one
Non-Functional:
List non-functional requirements for the system...
Need to save millions of short urls for a determined time
Need to handle different requests from millions of users
Capacity estimation
Estimate the scale of the system you are going to design...
API design
Define what APIs are expected from the system...
Database design
Defining the system data model early on will clarify how data will flow among different components of the system. Also you could draw an ER diagram using the diagramming tool to enhance your design...
High-level design
You should identify enough components that are needed to solve the actual problem from end to end. Also remember to draw a block diagram using the diagramming tool to augment your design...
Request flows
Explain how the request flows from end to end in your high level design. Also you could draw a sequence diagram using the diagramming tool to enhance your explanation...
Detailed component design
Dig deeper into 2-3 components and explain in detail how they work. For example, how well does each component scale? Any relevant algorithm or data structure you like to use for a component? Also you could draw a diagram using the diagramming tool to enhance your design...
Trade offs/Tech choices
Explain any trade offs you have made and why you made certain tech choices...
Failure scenarios/bottlenecks
Try to discuss as many failure scenarios/bottlenecks as possible.
Future improvements
What are some future improvements you would make? How would you mitigate the failure scenario(s) you described above?