How do I make class methods / properties in Swift?

They are called type properties and type methods and you use the class or static keywords.

class Foo {
    var name: String?           // instance property
    static var all = [Foo]()    // static type property
    class var comp: Int {       // computed type property
        return 42
    }

    class func alert() {        // type method
        print("There are \(all.count) foos")
    }
}

Foo.alert()       // There are 0 foos
let f = Foo()
Foo.all.append(f)
Foo.alert()       // There are 1 foos