ListDialogFragment.cs

using System.Collections.Generic;
using System.Linq;
using Android.App;
using Android.OS;
using SupportDialogFragment = Android.Support.V4.App.DialogFragment;

namespace Example.Android.App.Views.Base
{
	public class ListDialogFragment : SupportDialogFragment
	{
		public static readonly string TAG = "LIST_DIALOG";

		string _title;
		IList<string> _items;

		public static ListDialogFragment NewInstance(IList<string> items, string title)
		{
			ListDialogFragment frag = new ListDialogFragment();
			frag._items = items;
			frag._title = title;
			return frag;
		}

		public override Dialog OnCreateDialog(Bundle savedInstanceState)
		{
			AlertDialog.Builder builder = new AlertDialog.Builder(Activity);
			builder.SetTitle(_title)
				   .SetItems(_items.ToArray(), (sender, e) => { /* implement your item click listener here */ })
				   .SetCancelable(true)
				   .SetNegativeButton("Cancel", (sender, e) => { /* implement your Cancel button click listener here */ });

			return builder.Create();
		}
	}
}

//

// Show dialog fragment from activity

List<string> items = new List<string>();
// Add list items

ListDialogFragment frag = ListDialogFragment.NewInstance(items, "List title");
frag.Show(SupportFragmentManager, ListDialogFragment.TAG);