When ever I teach cryptography to beginners, they are confused with what you can do with the private and public key, in an asymmetric cryptographic scheme. I start by saying the your private key never leaves you, no matter what. No exception to the rules.
To help with the rest, I made this chart.
|Encryption (done by the sender)||Encrypt a message for an individual (that "message" is often a symmetric key)||Generate a digital signature (encrypt a document hash)|
|Decryption (done by the receiver)||Verify a digital signature (decrypt a hash of the message)||Decrypt a message destined to you (that "message is often a symmetric key)|
The colors in that chart indicate operations that are related to each other. To put it in words:
If you use a public key for encryption, you will use your private key for decryption.
If you use a private key for encryption, you will use a public key for decryption
But most students need some time to reach the asymmetric cryptography enlightenment. When they do reach it, I have to convince them that it is not the silver bullet it looks like. I found that remembering this chart helps them cram study for an exam.
Hope this helps !