A search API is way to build search without worrying about infrastructure management. A hosted search API like Algolia is capable of delivering real-time results, with relevance and speed within your websites, mobile, and voice applications.
The first step is to index your data in Algolia, in a proper format. Then, you can you can start testing the functionality with API calls or within the UI dashboard.
You can build all of this within your own tech-stack using official API clients or integrations.
There is a lot to creating a full search implementation, and the developer documentation walks you through every possibility.