Create a custom dialog with radio buttons list

A clean way is like this:

http://developer.android.com/guide/topics/ui/dialogs.html

Excerpt from (Adding a persistent multiple-choice or single-choice list)

mSelectedItems = new ArrayList();  // Where we track the selected items
AlertDialog.Builder builder = new AlertDialog.Builder(getActivity());
// Set the dialog title
builder.setTitle(R.string.pick_toppings)
// Specify the list array, the items to be selected by default (null for none),
// and the listener through which to receive callbacks when items are selected
       .setMultiChoiceItems(R.array.toppings, null,
                  new DialogInterface.OnMultiChoiceClickListener() {
           @Override
           public void onClick(DialogInterface dialog, int which,
                   boolean isChecked) {
               if (isChecked) {
                   // If the user checked the item, add it to the selected items
                   mSelectedItems.add(which);
               } else if (mSelectedItems.contains(which)) {
                   // Else, if the item is already in the array, remove it 
                   mSelectedItems.remove(Integer.valueOf(which));
               }
           }
       })
// Set the action buttons
       .setPositiveButton(R.string.ok, new DialogInterface.OnClickListener() {
           @Override
           public void onClick(DialogInterface dialog, int id) {
               // User clicked OK, so save the mSelectedItems results somewhere
               // or return them to the component that opened the dialog
               ...
           }
       })
       .setNegativeButton(R.string.cancel, new DialogInterface.OnClickListener() {
           @Override
           public void onClick(DialogInterface dialog, int id) {
               ...
           }
       });

return builder.create();

Read about http://developer.android.com/reference/android/app/AlertDialog.Builder.html#setSingleChoiceItems(int, int, android.content.DialogInterface.OnClickListener)

No custom view is necessary.

best and easy way......

void dialog(){

        AlertDialog.Builder alt_bld = new AlertDialog.Builder(this);
        //alt_bld.setIcon(R.drawable.icon);
        alt_bld.setTitle("Select a Group Name");
        alt_bld.setSingleChoiceItems(grpname, -1, new DialogInterface
                .OnClickListener() {
            public void onClick(DialogInterface dialog, int item) {
                Toast.makeText(getApplicationContext(),
                        "Group Name = "+grpname[item], Toast.LENGTH_SHORT).show();
                dialog.dismiss();// dismiss the alertbox after chose option

            }
        });
        AlertDialog alert = alt_bld.create();
        alert.show();


///// grpname is a array where data is stored... 


    }

Call showRadioButtonDialog() from the button.

This is just an example:

private void showRadioButtonDialog() {

 // custom dialog

  final Dialog dialog = new Dialog(this);
  dialog.requestWindowFeature(Window.FEATURE_NO_TITLE);
  dialog.setContentView(R.layout.dialog_layout);
  List<String> stringList=new ArrayList<>();  // here is list
      for(int i=0;i<2;i++) {
          if (i==0){
              stringList.add("Number Mode");
          }else {
              stringList.add("Character Mode");
          }

      }

      RadioGroup rg = (RadioGroup) dialog.findViewById(R.id.radioGroup);

      for(int i=0;i<stringList.size();i++){
            RadioButton rb=new RadioButton(this); // dynamically creating RadioButton and adding to RadioGroup.
            rb.setText(stringList.get(i));
            rg.addView(rb);
      }
}

Your layout view might be:radiobutton_dialog.xml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
   android:layout_width="match_parent"
   android:layout_height="match_parent"
   android:orientation="vertical">
      <RadioGroup
          android:id="@+id/radio_group"
          android:layout_width="wrap_content"
          android:layout_height="match_parent"
          android:layout_gravity="center_vertical"
          android:orientation="vertical">
    </RadioGroup>
 </LinearLayout>

Note: you can customize your dialog view (like setting title, message etc.)

Edit: To retrieving value of the selected RadioButton you have to implement setOnCheckedChangeListener listener for your RadioGroup as :

 rg.setOnCheckedChangeListener(new RadioGroup.OnCheckedChangeListener() {

            @Override
            public void onCheckedChanged(RadioGroup group, int checkedId) {
                 int childCount = group.getChildCount();
                 for (int x = 0; x < childCount; x++) {
                    RadioButton btn = (RadioButton) group.getChildAt(x);
                    if (btn.getId() == checkedId) {
                         Log.e("selected RadioButton->",btn.getText().toString());

                    }
                 }
            }
        });