My problem is I don't know how to read data from the serial,
Use Serial.available() to know how much data there is. If there is any, use Serial.read to read the next character.
save it as a string
Define a character array and an index. When you have data to store, store it in the position pointed to by the index and increment the index. Store a NULL ('\0') then. The string should be kept NULL terminated at all times, in my opinion. It MUST be NULL terminated before any string functions are called with it as input.
parse the information
Use strtok() (not strtok_r()). You may need/want atoi() and/or atof(), too.
and print that information to the LCD.
Depends on the LCD.
What you want to do is covered by the examples that come with the IDE. It is up to you to understand what each example does, and how to combine them into one usable sketch.