Regarding Casascius Bitcoins. I know the visible numbers and letters on the back of the coin is the "public key" & that the "private key" is under the sticker. I am not planning on redeeming any tokens but I am interested in knowing the technical process for how to redeem them.

If someone has a bitcoin written out as a long sequence of numbers and letters on a piece of paper, how can that long sequence of numbers and letters be sent to an exchange or a digital wallet?

I would like a deeper understanding. Thanks!