I came across this because I started using Zillow this morning. The Zillow API is surprisingly easy which might be why I haven't found a step-by-step tutorial yet.
First, here's the URL to where I got my information: http://www.zillow.com/howto/api/GetZestimate.htm
Next, you'll need to register and get a ZWSID. It took me about 5 minutes to register and less than a minute to get a response from Zillow with my ZWSID
To do your first query, take this 'http://www.zillow.com/webservice/GetZestimate.htm?zws-id=&zpid=48749425' and replace with your own ID. Then copy and paste the edited URL into a browser or Fiddler and execute the query.
If you want to query a specific address put a '-' instead of a space. So the URL would look something like this: http://www.zillow.com/webservice/GetSearchResults.htm?zws-id=&address=123-Main-Street&citystatezip=55555
I will always have the zip and they query will work if you only provide the zip code. It will also work if you just provide the city and state. (Remember to replace the space with a '-')
I have found that abbreviations and spelling the complete word works. For example: 123-Main-St and 123-Main-Street worked equally as well.
As an FYI, the API only returns XML and not JSON. (http://www.zillow.com/advice-thread/Is-there-a-way-to-get-API-data-in-JSON-format-If-not-is-there-any-plan-to-add-JSON-as-an-option/494343/)
So I think that answers the first part of your question.
For the second part, I would suggest that you create a new question. I think you'll get a lot more answers if you narrow down the question you're asking. As it is, it's a really broad question and would require a lot more information. Starting with more detail about the environment you're developing in: ASP.net, PHP, where will the query be executed etc.