How to get elements from Json array in PostgreSQL

I'm not sure you have a json[] (PostgreSQL array of json values) typed column, or a json typed column, which appears to be a JSON array (like in your example).

Either case, you need to expand your array before querying. In case of json[], you need to use unnest(anyarray); in case of JSON arrays in a json typed column, you need to use json_array_elements(json) (and LATERAL joins -- they are implicit in my examples):

select     t.id,
           each_section ->> 'name' section_name,
           each_attribute ->> 'attrkey3' attrkey3
from       t
cross join unnest(array_of_json) each_section
cross join json_array_elements(each_section -> 'attributes') each_attribute
where      (each_attribute -> 'attrkey3') is not null; 
-- use "where each_attribute ? 'attrkey3'" in case of jsonb


select     t.id,
           each_section ->> 'name' section_name,
           each_attribute ->> 'attrkey3' attrkey3
from       t
cross join json_array_elements(json_array) each_section
cross join json_array_elements(each_section -> 'attributes') each_attribute
where      (each_attribute -> 'attrkey3') is not null;

SQLFiddle

Unfortunately, you cannot use any index with your data. You need to fix your schema first, in order to do that.

If you wish to access a single element then use json_array -> index

For example, if you have json_arr=[1,2,3] then json_array -> 0 will return 1

And also, if there was a key value map data in array:

select each_data -> 'value' as value3 
from t cross join jsonb_array_elements(t.sections -> 'attributes') each_attribute 
where each_attribute -> 'key' = '"attrkey3"'

I am mentioning this because the great answer also provided a perfect solution for my case. By the way, also be aware of jsonb_array.. method for jsonb type attribute.