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An Objective-C class needs an interface (header) and implementation:

#import <Foundation/Foundation.h>

@interface Point : NSObject
{
    int _x;
    int _y;
}
@property int x;
@property int y;
- (double)distanceFrom:(Point *)other;
@end

@implementation Point
@synthesize x = _x, y = _y;
- (double)distanceFrom:(Point *)other {
    int dx = self.x - other.x;
    int dy = self.y - other.y;
    return sqrt(dx * dx + dy * dy);
}
@end

• @interface ClassName : Superclass -- declares the class
• @property -- declares that the class exposes a getter/setter for a value
• - (returnType)methodName... -- instance method (the -)
• + (returnType)methodName... -- class method (the +)
• @end closes the block
• self is the receiver inside a method (like this)

Important -- explicit synthesis. Modern Apple Clang auto-generates a backing ivar and accessor methods for every @property, so you can skip @synthesize entirely. This judge runs on the GNUstep runtime, which does not auto-synthesize. If you only write @property int x; and then use self.x, the code compiles fine but crashes at runtime with something like does not recognize selector setX:.

Always declare an explicit backing ivar and synthesize it yourself:

@interface Point : NSObject
{
    int _x;   // backing ivar
}
@property int x;
@end

@implementation Point
@synthesize x = _x;   // wires self.x / self.x = ... to _x
@end

Creating instances:

Point *p = [[Point alloc] init];
p.x = 3;
p.y = 4;

The [Class alloc] allocates memory; init initializes. Modern code may use [Class new] which combines them. Wrap your main body in @autoreleasepool { ... } when working with Objective-C objects.