Use an OpenPGP implementation such as GnuPG to do the following. Note that no email is involved—you are working exclusively with files on a single machine.

(a) Generate a public–private key pair.

(b) Use your public key to encrypt a file, as if for secure storage, and then use your private key to decrypt it.

(c) Use your key pair to digitally sign an unencrypted file and then, as if you were someone else, verify your signature using your public key.

(d) Consider the first public–private key pair as belonging to Alice, and generate a second public–private key pair, for Bob. Playing the role of Alice, encrypt and sign a file intended for Bob. (Be sure to sign as Alice, not Bob.) Then, playing the role of Bob, verify Alice’s signature and decrypt the file.