I thought I'd share a code snippet where I show a UIPickerView when you click a UITextField. The code uses a UIPickerView, but there's no reason to use a different view controller, like a UITableViewController that uses a table instead of a picker.

Just create a single-view project with a nib, and add a UITextField to the view and make you connections in IB.

// .h file #import

@interface MyPickerViewViewController : UIViewController <UIPickerViewDelegate,
                                                      UIPickerViewDataSource,
                                                      UITextFieldDelegate>

- (IBAction)dismissPickerView:(id)sender;

@end

// .m file

#import "MyPickerViewViewController.h"

@interface MyPickerViewViewController () {
    UIPickerView *_pv;
    NSArray *_array;
    IBOutlet __weak UITextField *_tf;
    BOOL _pickerViewShown;
}

@end

@implementation MyPickerViewViewController

- (void)viewDidLoad
{
    [super viewDidLoad];

    _pickerViewShown = NO;
    _array = [NSArray arrayWithObjects:@"One", @"Two", @"Three", @"Four", nil];

    _pv = [[UIPickerView alloc] initWithFrame:CGRectZero];
    _pv.showsSelectionIndicator = YES;
    _pv.dataSource = self;
    _pv.delegate = self;
    _tf.delegate = self;
    _tf.inputView = _pv;
}

- (IBAction)dismissPickerView:(id)sender
{
    [_pv removeFromSuperview];
    [_tf.inputView removeFromSuperview];
    [_tf resignFirstResponder];
    _pickerViewShown = NO;
}

- (void)didReceiveMemoryWarning
{
    [super didReceiveMemoryWarning];
    // Dispose of any resources that can be recreated.
}

- (BOOL)textFieldShouldBeginEditing:(UITextField *)textField
{
    if (!_pickerViewShown) {
        [self setRectForPickerViewRelativeToTextField:textField];
        [self.view addSubview:_tf.inputView];
        _pickerViewShown = YES;
    }
    else {
        [self dismissPickerView:self];
    }
    return NO;
}

- (void)setRectForPickerViewRelativeToTextField:(UITextField*)textField
{
    CGFloat xPos = textField.frame.origin.x;
    CGFloat yPos = textField.frame.origin.y;
    CGFloat width = textField.frame.size.width;
    CGFloat height = textField.frame.size.height;
    CGFloat pvHeight = _pv.frame.size.height;
    CGRect pvRect = CGRectMake(xPos, yPos+height, width, pvHeight);
    _pv.frame = pvRect;
}

- (NSString *)pickerView:(UIPickerView *)pickerView titleForRow:(NSInteger)row forComponent:(NSInteger)component
{
    return [_array objectAtIndex:row];
}

- (NSInteger)numberOfComponentsInPickerView:(UIPickerView *)pickerView
{
    return 1;
}

- (NSInteger)pickerView:(UIPickerView *)pickerView numberOfRowsInComponent:(NSInteger)component
{
    return _array.count;
}

- (void) pickerView:(UIPickerView *)pickerView didSelectRow:(NSInteger)row inComponent:(NSInteger)component
{
    _tf.text = [_array objectAtIndex:row];
    [self dismissPickerView:self];
}

@end