You need to have a fully functioning Ethereum node to test these APIs. By default, both geth and Parity expose port 8545 for JSON-RPC. Some examples are given in JavaScript, but you can use any programming language that supports HTTPS requests.

Make sure that you are starting your geth node with enough --rpcapi permissions:

$ geth --rpc --rpcapi "web3,eth,personal"

We will focus on a few important APIs here and you can always find the complete list for reference at github.com/ethereum/wiki/wiki/JSON-RPC.