I solved this by adding a category to NSMutableArray.

Edit: Removed unnecessary method thanks to answer by Ladd.

Edit: Changed (arc4random() % nElements) to arc4random_uniform(nElements) thanks to answer by Gregory Goltsov and comments by miho and blahdiblah

Edit: Loop improvement, thanks to comment by Ron

Edit: Added check that array is not empty, thanks to comment by Mahesh Agrawal

//  NSMutableArray_Shuffling.h

#if TARGET_OS_IPHONE
#import <UIKit/UIKit.h>
#else
#include <Cocoa/Cocoa.h>
#endif

// This category enhances NSMutableArray by providing
// methods to randomly shuffle the elements.
@interface NSMutableArray (Shuffling)
- (void)shuffle;
@end


//  NSMutableArray_Shuffling.m

#import "NSMutableArray_Shuffling.h"

@implementation NSMutableArray (Shuffling)

- (void)shuffle
{
    NSUInteger count = [self count];
    if (count <= 1) return;
    for (NSUInteger i = 0; i < count - 1; ++i) {
        NSInteger remainingCount = count - i;
        NSInteger exchangeIndex = i + arc4random_uniform((u_int32_t )remainingCount);
        [self exchangeObjectAtIndex:i withObjectAtIndex:exchangeIndex];
    }
}

@end

Compare method

Either you implement a compare-method for your object:

- (NSComparisonResult)compare:(Person *)otherObject {
    return [self.birthDate compare:otherObject.birthDate];
}

NSArray *sortedArray = [drinkDetails sortedArrayUsingSelector:@selector(compare:)];

NSSortDescriptor (better)

or usually even better:

NSSortDescriptor *sortDescriptor;
sortDescriptor = [[NSSortDescriptor alloc] initWithKey:@"birthDate"
                                           ascending:YES];
NSArray *sortedArray = [drinkDetails sortedArrayUsingDescriptors:@[sortDescriptor]];

You can easily sort by multiple keys by adding more than one to the array. Using custom comparator-methods is possible as well. Have a look at the documentation.

Blocks (shiny!)

There's also the possibility of sorting with a block since Mac OS X 10.6 and iOS 4:

NSArray *sortedArray;
sortedArray = [drinkDetails sortedArrayUsingComparator:^NSComparisonResult(Person *a, Person *b) {
    return [a.birthDate compare:b.birthDate];
}];

Performance

The -compare: and block-based methods will be quite a bit faster, in general, than using NSSortDescriptor as the latter relies on KVC. The primary advantage of the NSSortDescriptor method is that it provides a way to define your sort order using data, rather than code, which makes it easy to e.g. set things up so users can sort an NSTableView by clicking on the header row.