First you need to make a CredentialsProvider

UsernamePasswordCredentials u =
new UsernamePasswordCredentials("some username", " some password");
CredentialsProvider creds =
new BasicCredentialsProvider();
creds.setCredentials(
new AuthScope("crossbrowsertesting.com", AuthScope.ANY_PORT),
u);

Next you would create your HttpClient like normal but you add the credential object you created above

DefaultHttpClient httpclient = new DefaultHttpClient();
httpclient.setCredentialsProvider(creds);

Then you should be able to call execute

HttpResponse response = httpclient.execute(httpget);

And that should be it. The URL that you will be requesting will look something like this:

http://crossbrowsertesting.com/api/screenshots/9999/version/9999/show

You will need to change it to match your own case.