Estimate the scale of the system you are going to design...
Assumption: front end will handle actual redirection using the original URL
Because we are only concerned with two values (the original URL and the short URL), we can use a key-value store, where key is short URL and value is original URL. NoSQL works well for this and is easy to scale.
You should identify enough components that are needed to solve the actual problem from end to end.
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...
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?
Explain any trade offs you have made and why you made certain tech choices...
Try to discuss as many failure scenarios/bottlenecks as possible.
What are some future improvements you would make? How would you mitigate the failure scenario(s) you described above?