To add a char to a string, you must have a string and an index to that string.
char myString[20];
byte myStringIndex;
Then you can add to your string as long as there is still room.
If (myStringIndex < 19) {
myString[myStringIndex] = inChar;
myStringIndex++;
}
Whenever you feel like it, you can print the string.
Serial.print (myString);
This is covered in Serial Input Basics.