The format for datetimes in this API follows the ISO 8601 format. This format will work when passed in for the query syntax as well as on request bodies for POST/PUT requests.
There are a couple of common variations to this format: one with the timezone offset, and one without.
2014-05-12T00:00:00.0Z
2014-05-13T06:00:00.000-06:00
Libraries like RestSharp and JSON.NET will handle this format for you.
DateTime.UtcNow.ToString("s") // NOTE: DateTime.Now.ToString("s") will give local time without the offset
DateTime.Now.ToString("yyyy-MM-dd'T'HH:mm:ss.FFFFFFK")
>>> from datetime import datetime
>>> datetime.utcnow().isoformat()
'2014-05-12T14:51:02.206277'
irb(main):001:0> require 'time'
=> true
irb(main):002:0> Time.now.iso8601
=> "2014-05-12T09:47:09-05:00"
irb(main):003:0> Time.now.utc.iso8601
=> "2014-05-12T14:47:16Z"
> var date = new Date();
undefined
> date.toISOString();
'2014-05-12T14:53:34.524Z'