Here's how it works:
* The first part describes the cause or reason ("the rain")
* The phrase "as a result of" connects the cause to the effect
* The second part describes the effect or outcome ("the picnic was canceled")
Example:
> The rain was heavy and relentless. As a result of the downpour, the picnic was canceled.
Here are some other ways to say "as a result of":
* Because of
* Due to
* Owing to
* Consequently
* Therefore
* Hence
In essence, "as a result of" indicates a causal relationship between two events.