Is there an easy way to create a drop down menu for a UITextField, so that the user can type a custom entry or select one from a list?
For drop down menu you can implement UITableView. You can populate this UItableview with your list.
Just declare it in ViewDidLoad method of your ViewController and then you can show or hid accordingly later.
TableView = [[UITableView alloc]initWithFrame:CGRectMake(x,x,x,x) ];
TableView.delegate = self;
TableView.dataSource = self;
Add this to main view when user clickes on UITextField.
[self.view addSubView:TableView];
If you want user to select from given list only better option is UIButton instead of UITextField.
EDIT: I didn't notice it is the same as above answer.