As of the current Babylon protocol and the upcoming Carthage, the RPC only provides you the ability to retrieve the value for a known key that you provide to the RPC. But even in this scenario you need to provide not the readable key you stored, but a hash of that key as that is how it is represented internally. This answer describes how to call the RPC
The RPC does not provide a means to "get all keys" or to "get all values". To accomplish this you must do an impractical amount of parsing so it is recommended that you use either an indexer or a library to do most of the work for you.
For single key lookup, Taquito library allows you to do the following:
const contract = await Tezos.contract.at("KT1...")
const storage = await contract.storage()
const bigMapDetail = await storage.namedbigmap.get("readable lookup key")
Read more on Taquito and big maps at https://medium.com/tezoscommons/new-taquito-release-now-with-bigmaps-7d7352351af4
To get all the values, the tzStats indexer provides an easy to use API (soon other indexers are likely to add this as well). Example TzStats call to get all the values out of a contract with a big map:
curl "https://api.tzstats.com/explorer/bigmap/17/values"
Read more on tzStats big map support at https://tzstats.com/blog/tezos-smart-contract-apis/
You can also use PyTezos "big_map_get" to do some of the heavy lifting for you if you don't want to rely on an indexer. https://baking-bad.github.io/pytezos/