Just the same as stamps have always worked. You stick them on your envelopes and put them in a post box. However you have to make sure that you attach the bar code, as well as the stamp, as that's the bit that Royal Mail's machines will read to check that the correct postage has been paid. (The present machinery examines almost invisible phosphor bands on stamps in order to see their values but that system is less secure than the new one).
The bar codes (which are actually closer to 'QR' codes than to true bar codes) also come with additional features, such as being able to be scanned by the recipient to view a video, but those features are entirely optional and don't affect the way that the stamps are actually used.
https://www.royalmail.com/sending/barcoded-stamps