You should be able to simply do this:
Context context = new InitialContext();
dataSource = (javax.sql.DataSource) context.lookup("jdbc/myDataSource");
If you are looking it up from a remote destination you need to use the WL initial context factory like this:
Hashtable<String, String> h = new Hashtable<String, String>(7);
h.put(Context.INITIAL_CONTEXT_FACTORY, "weblogic.jndi.WLInitialContextFactory");
h.put(Context.PROVIDER_URL, pURL); //For example "t3://127.0.0.1:7001"
h.put(Context.SECURITY_PRINCIPAL, pUsername);
h.put(Context.SECURITY_CREDENTIALS, pPassword);
InitialContext context = new InitialContext(h);
dataSource = (javax.sql.DataSource) context.lookup("jdbc/myDataSource");