accessing static resource in apex

You can simply query them.

StaticResource sr = [SELECT Id, Body FROM StaticResource WHERE Name = 'MyJsonFile' LIMIT 1];
String body = sr.Body.toString();

Access Static Resource

If you want to get some file from zipped static resource, you can use getContent():

StaticResource static_resource = [SELECT Id, SystemModStamp
                                  FROM StaticResource 
                                  WHERE Name = 'My Zip Array'
                                  LIMIT 1];
String url_file_ref = '/resource/'
                    + String.valueOf(((DateTime)static_resource.get('SystemModStamp')).getTime())
                    + '/' 
                    + static_resource.get('Name')
                    + '/myfile.json';
PageReference file_ref = new PageReference(url_file_ref);
String res_json_body = file_ref.getContent().toString();

Please, remember, you can not always use this due to limitation on getContent() (it can not be used in triggers) and latest salesforce updates.

References:

• https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_System_PageReference_getContent.htm

You can also use the PageReference.forResource() method, then add the path/filename onto it.

String myUrl = PageReference.forResource('MyStaticResource').getUrl();
myUrl = myUrl.subString(0, myUrl.indexOf('?'));
system.debug(myUrl + '/path/myImage.png');

PageReference.forResource('MyStaticResource').getUrl() return a string with the base URL and a number of parameters you don't need, which is why I've used the subString method.