In modern cryptography, asymmetric encryption schemes are used to exchange a shared key used by the symmetric encryption which is used for actual data encryption. This is because asymmetric encryption schemes require more processor resources and longer computational time compared with symmetric encryption. In another word, asymmetric encryption encrypts symmetric encryption key, symmetric encryption encrypts data.
You are right, there are some plain text while the parties try to establish a 'connection'. That is where the magic of the mathematics comes in, asymmetric encryption is based on the well-known mathematical difficult problems(ex. RSA based on big integer factorisation, Diffie-Hellman Key Exchange based on discrete logarithm problem, ECC is based on elliptic curves over finite fields problem). The properties of mathematical difficult problems have made the shared symmetric key safe even in the form of plain text. I suggest you start from Diffie-Hellman Key Exchange, Wikipedia has a fairly easy article to read(https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange).
If you want to learn cryptography from scratch, I suggest the book called "Introduction to Modern Cryptography, Second Edition By Jonathan Katz" for you, it involves most modern cryptography technologies and easy to understand even for a beginner.