I've built some google reader integration in python but I can share some of the api knowledge so you can get started. output=json is also available for all.
Login: https www.google.com/accounts/ClientLogin
POST &email=email&passwd=password&service=reader&source=appname&continue=http://www.google.com
from the response grab Auth=
Next hit: www.google.com/reader/api/0/token
HEADER Authorization=GoogleLogin auth=$Auth
That response becomes $token for the session.
From there it's just hitting some url's always passing that auth header and including the token in the querystring or post.
Gets a list of your subscriptions: www.google.com/reader/api/0/subscription/list?output=xml
To modify subscriptions this is the base url plus some post data for the action to perform
www.google.com/reader/api/0/subscription/edit?pos=0&client=$source
POST to add: s=$streams&t=$title&T=$token&ac=subscribe
POST to remove: s=$stream&T=$token&ac=unsubscribe
The $stream is generally feed/$feedurl like this for techcrunch, feed/http:// feeds.feedburner.com/Techcrunch
Sorry had to mangle some of the urls cause i don't have enough rep yet.
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