Finish activity in dialog class

You can finish your Activity as below...

Intent intent = new Intent(context, YourSecondActivity.class);
context.startActivity(intent);
((Activity) context).finish();

Update:

In your constructor of you custom dialog class, get the activity context as below...

Context mContext;

public myDialog(Context context) {
    super(context);
    this.mContext = context;
}

then in your onClick() method finish the activity as below...

@Override
public void onClick(View v) {

    Intent menu = new Intent(mContext, menu.class);
    mContext.startActivity(menu);
    ((Activity) mContext).finish();
}

Firstly in your dialog class pass the context of the caller activities say MainActivit.class context

Now first close the dialog

//so as to avoid the window leaks as on destroying the activity it's context would also get vanished.
    dialog.dismiss();

and then

((Activity) context).finish();