United States Postal Service:
This shipping method is currently unavailable. If you would like to ship using this shipping method, please contact us.

This is because you aren’t getting proper access to the USPS API. Magento, by default comes with the following URL set up in the shipping configuration for USPS:
http://production.shippingapis.com/ShippingAPI.dll

The problem is that by default, you don’t have access to USPS’s production API. They have to approve you first. Keep in mind that they only allow you to use it on one web site per account, so if you’re setting Magento up for a client, customer, or other business entity other than your own you should set up a separate USPS account for them.

You can set up your USPS WebTools account here:
http://www.usps.com/webtools/

Once you have set up your account, they will give you access to the testing environment. The URL for the USPS test API is:
http://testing.shippingapis.com/ShippingAPITest.dll

Now, before you paste that into Magento, you should be aware that the USPS test environment only supports very specific data. According to their own documentation:

ZipOrigination: 10022
ZipDestination: 20008 (is set during Checkout process by user)
Pounds: 10
Ounces: 5 (weight can be set for every product on Administration > Products)
Size: LARGE
Machinable: TRUE

To test international shipping use the following values:

Pounds: 2
Ounces: 0
MailType: Package
Country: Albania

or

Pounds: 0
Ounces: 1
MailType: Postcards or Aerogrammes
Country: Algeria

All other parameters’ values won’t work in the test environment.

This is why most Magento consultants and installation service providers typically just ask USPS to turn on production mode. When you are approved by USPS for the production API, you should use the following URL:
http://production.shippingapis.com/ShippingAPI.dll

But remember, it’s very important that you set up a separate USPS account for each Magento web site (or at least one per domain). USPS will disable your access to their production server if you are caught using your account on multiple web sites. That would make all of your Magento customers very upset, all at the same time.

To request access to the USPS production API, fill out the form here:
http://www.usps.com/webtools/webtoolsapirequestform.htm

Be sure that in your request, you explain that you are using third party software (Magento) and that you only want access to the API so that you can calculate shipping costs associated with using USPS.

If you leave out this information they will reject your request or ask you to submit a valid test before they give you access. Third party software doesn’t need to be tested as long as you tell them you are using Magento.

USPS doesn’t allow you to use their API for batch processing or data cleansing, so be sure to NOT check these boxes on the request form.

Once USPS gives you access to their production API server, Magento should work with all USPS shipping options. If you are still having trouble, check that you have access to USPS’s production API server.

USPS Tech Support: 1-800-344-7779 (7:00 AM to 11:00 PM EST daily)

Once you have it correctly configured and you have access to the production API, you should be able to place an order and check out to see a list of USPS shipping options with the costs of each calcualted based on the weight of the product you are ordering.

You will need to remove shipping options that are irrelevant, for example USPS Library Mail is only for shipping academic things like books between academic institutions or libraries.

Click here to read about different shipping methods such as Parcel Post.