How do I query using fields inside the new PostgreSQL JSON datatype?

Postgres 9.2

I quote Andrew Dunstan on the pgsql-hackers list:

At some stage there will possibly be some json-processing (as opposed to json-producing) functions, but not in 9.2.

Doesn't prevent him from providing an example implementation in PLV8 that should solve your problem. (Link is dead now, see modern PLV8 instead.)

Postgres 9.3

Offers an arsenal of new functions and operators to add "json-processing".

• The manual on new JSON functionality.
• The Postgres Wiki on new features in pg 9.3.

The answer to the original question in Postgres 9.3:

SELECT *
FROM   json_array_elements(
  '[{"name": "Toby", "occupation": "Software Engineer"},
    {"name": "Zaphod", "occupation": "Galactic President"} ]'
  ) AS elem
WHERE elem->>'name' = 'Toby';

Advanced example:

• Query combinations with nested array of records in JSON datatype

For bigger tables you may want to add an expression index to increase performance:

• Index for finding an element in a JSON array

Postgres 9.4

Adds jsonb (b for "binary", values are stored as native Postgres types) and yet more functionality for both types. In addition to expression indexes mentioned above, jsonb also supports GIN, btree and hash indexes, GIN being the most potent of these.

• The manual on json and jsonb data types and functions.
• The Postgres Wiki on JSONB in pg 9.4

The manual goes as far as suggesting:

In general, most applications should prefer to store JSON data as jsonb, unless there are quite specialized needs, such as legacy assumptions about ordering of object keys.

Bold emphasis mine.

Performance benefits from general improvements to GIN indexes.

Postgres 9.5

Complete jsonb functions and operators. Add more functions to manipulate jsonb in place and for display.

• Major good news in the release notes of Postgres 9.5.

With Postgres 9.3+, just use the -> operator. For example,

SELECT data->'images'->'thumbnail'->'url' AS thumb FROM instagram;

see http://clarkdave.net/2013/06/what-can-you-do-with-postgresql-and-json/ for some nice examples and a tutorial.