I need to know if I can select some text and copy it, and then paste it on an Apple Watch.
No, there is no such functionality on Apple Watch as standard as there are no text fields for entering text other than dictation.
I realize that this question has already been answered, but I wanted to contribute something I've found useful on the topic.
While you may not be able to copy or paste at the time, there have been many efforts to create keyboards for Apple Watch. For example, a rather intuitive one (though it's not available on the Apple Watch yet) is Lunate, which uses a circular typing interface. There's also Weboard, which is still in development, but plans to use motion sensors to change which row of the keyboard you're viewing when you tilt your wrist, displaying one row at a time.
Those apps aim to be keyboards independently, but there are a host of apps on the App Store that have functionalities like texting and searching the web while offering keyboards, no matter how intuitive. Try tinynote for jotting down notes, WatchWeb for web browsing, Next for Twitter, and eyeFree Messenger for texting. Most options are based on either Morse Code or a list of letters that you scroll through with the Digital Crown.