In order to access private fields, you need to get them from the class's declared fields and then make them accessible:

Field f = obj.getClass().getDeclaredField("stuffIWant"); //NoSuchFieldException
f.setAccessible(true);
Hashtable iWantThis = (Hashtable) f.get(obj); //IllegalAccessException

EDIT: as has been commented by aperkins, both accessing the field, setting it as accessible and retrieving the value can throw Exceptions, although the only checked exceptions you need to be mindful of are commented above.

The NoSuchFieldException would be thrown if you asked for a field by a name which did not correspond to a declared field.

obj.getClass().getDeclaredField("misspelled"); //will throw NoSuchFieldException

The IllegalAccessException would be thrown if the field was not accessible (for example, if it is private and has not been made accessible via missing out the f.setAccessible(true) line.

The RuntimeExceptions which may be thrown are either SecurityExceptions (if the JVM's SecurityManager will not allow you to change a field's accessibility), or IllegalArgumentExceptions, if you try and access the field on an object not of the field's class's type:

f.get("BOB"); //will throw IllegalArgumentException, as String is of the wrong type

Yes, it absolutely is - assuming you've got the appropriate security permissions. Use Field.setAccessible(true) first if you're accessing it from a different class.

import java.lang.reflect.*;

class Other
{
    private String str;
    public void setStr(String value)
    {
        str = value;
    }
}

class Test
{
    public static void main(String[] args)
        // Just for the ease of a throwaway test. Don't
        // do this normally!
        throws Exception
    {
        Other t = new Other();
        t.setStr("hi");
        Field field = Other.class.getDeclaredField("str");
        field.setAccessible(true);
        Object value = field.get(t);
        System.out.println(value);
    }
}

And no, you shouldn't normally do this... it's subverting the intentions of the original author of the class. For example, there may well be validation applied in any situation where the field can normally be set, or other fields may be changed at the same time. You're effectively violating the intended level of encapsulation.

You have do like this,

public class A {
    private B b = new B();

    class B {
        private String value = "String";
    }
}

public class ClassB {
    public static void main(String args[]) throws NoSuchFieldException, SecurityException, IllegalArgumentException, IllegalAccessException{
        A obj = new A();
        Field f = obj.getClass().getDeclaredField("b"); 
        f.setAccessible(true);
        A.B b = (B) f.get(obj);
        Field f2 = b.getClass().getDeclaredField("value");
        f2.setAccessible(true);
        String value = (String) f2.get(b);
        System.out.println(value);
    }
}

What you are missing is to setAccessible(true) to inner class field.

1) How can I access the private methods and the private data members?

You can do it with a little help of the setAccessible(true) method:

class Dummy{
    private void foo(){
        System.out.println("hello foo()");
    }
    private int i = 10;
}

class Test{
    public static void main(String[] args) throws Exception {
        Dummy d = new Dummy();

        /*---  [INVOKING PRIVATE METHOD]  ---*/
        Method m = Dummy.class.getDeclaredMethod("foo");
        //m.invoke(d); // Exception java.lang.IllegalAccessException
        m.setAccessible(true);//Abracadabra
        m.invoke(d); // Now it's OK

        /*---  [GETING VALUE FROM PRIVATE FIELD]  ---*/
        Field f = Dummy.class.getDeclaredField("i");
        //System.out.println(f.get(d)); // Not accessible now
        f.setAccessible(true); // Abracadabra
        System.out.println(f.get(d)); // Now it's OK

        /*---  [SETTING VALUE OF PRIVATE FIELD]  ---*/
        Field f2 = Dummy.class.getDeclaredField("i");
        //f2.set(d,20); // Not accessible now
        f2.setAccessible(true); // Abracadabra
        f2.set(d, 20); // Now it's OK
        System.out.println(f2.get(d));
    }
}

2) Is it possible to access a local variable via reflection?

No. Local variables cannot be accessed outside of a block in which they were created (someone could say that you can assign such a variable to a field like field = localVariable; and later access such a field via reflection, but this way we will be accessing the value, not the variable).

3) Is there any way to prevent anyone from accessing private constructors, methods, and data members?

I think for constructors or methods you could use stacktrace to check if it was invoked by Reflection.
For fields I can't find a solution to prevent accessing them via reflection.

[WARNING: This is not approved by anyone. I just wrote it inspired by your question.]

class Dummy {
    private void safeMethod() {
        StackTraceElement[] st = new Exception().getStackTrace();
        // If a method was invoked by reflection, the stack trace would be similar
        // to something like this:
        /*
        java.lang.Exception
            at package1.b.Dummy.safeMethod(SomeClass.java:38)
            at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
            at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
            at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
        ->    at java.lang.reflect.Method.invoke(Method.java:601)
            at package1.b.Test.main(SomeClass.java:65)
        */
        //5th line marked by "->" is interesting one so I will try to use that info

        if (st.length > 5 &&
            st[4].getClassName().equals("java.lang.reflect.Method"))
            throw new RuntimeException("safeMethod() is accessible only by Dummy object");

        // Now normal code of method
        System.out.println("code of safe method");
    }

    // I will check if it is possible to normally use that method inside this class
    public void trySafeMethod(){
        safeMethod();
    }

    Dummy() {
        safeMethod();
    }
}

class Dummy1 extends Dummy {}

class Test {
    public static void main(String[] args) throws Exception {
        Dummy1 d1 = new Dummy1(); // safeMethod can be invoked inside a superclass constructor
        d1.trySafeMethod(); // safeMethod can be invoked inside other Dummy class methods
        System.out.println("-------------------");

        // Let's check if it is possible to invoke it via reflection
        Method m2 = Dummy.class.getDeclaredMethod("safeMethod");
        // m.invoke(d);//exception java.lang.IllegalAccessException
        m2.setAccessible(true);
        m2.invoke(d1);
    }
}

Output from Test main method:

code of safe method
code of safe method
-------------------
Exception in thread "main" java.lang.reflect.InvocationTargetException
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
    at java.lang.reflect.Method.invoke(Method.java:601)
    at package1.b.Test.main(MyClass2.java:87)
Caused by: java.lang.RuntimeException: method safeMethod() is accessible only by Dummy object
    at package1.b.Dummy.safeMethod(MyClass2.java:54)
    ... 5 more

To access a private field you need to set Field::setAccessible to true. You can pull the field off the super class. This code works:

CopyClass<?> clazz = Child.class;
Object cc = clazz.newInstance();

Field f1 = cc.getClass().getSuperclass().getDeclaredField("a_field");
f1.setAccessible(true);
f1.set(cc, "reflecting on life");
String str1 = (String) f1.get(cc);
System.out.println("field: " + str1);