There isn't, as others have already said, such a thing as a private method in Objective-C. However, starting in Objective-C 2.0 (meaning Mac OS X Leopard, iPhone OS 2.0, and later) you can create a category with an empty name (i.e. @interface MyClass ()) called Class Extension. What's unique about a class extension is that the method implementations must go in the same @implementation MyClass as the public methods. So I structure my classes like this:

In the .h file:

@interface MyClass {
    // My Instance Variables
}

- (void)myPublicMethod;

@end

And in the .m file:

@interface MyClass()

- (void)myPrivateMethod;

@end

@implementation MyClass

- (void)myPublicMethod {
    // Implementation goes here
}

- (void)myPrivateMethod {
    // Implementation goes here
}

@end

I think the greatest advantage of this approach is that it allows you to group your method implementations by functionality, not by the (sometimes arbitrary) public/private distinction.

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.