How really big applications (such as facebook) scale their database I am curious of how one will scale huge database for example facebook DB. What I know is the application is deployed somehow to multiple data centers which means that each "node" in each data center should have fast access to that big DB.

On first place I can not image how they do deploys but that is another question (I guess?).

So if I am not wrong the question is how so many separate nodes access huge database and everything is consistent, stable, well-performing and scalable?
These companies use a mix of commercial products and new technologies developed in-house. Many are documented. Several are open source. The larger companies maintain separate research organisations to bring along the next generation of products. Many papers are available and make for interesting reading.

Broadly, the NoSQL movement was driven by these organisations' needs that could not be met by products available at the time. Cassandra, DynamoDB and LevelDB, amongst others, came from this movement. More recently NewSQL has emerged, giving global scale and ACID guarantees. One example is Google Spanner.