How are "string-messages" converted to "number-messages"?
Cryptographic schemes handle byte strings. To convert a string to a byte string, you need some encoding like ASCII (which can't handle every character) or UTF-8 (which can handle the entire Unicode).

Some specific schemes, like RSA, do need to interpret the byte string as a number. This process is defined in the scheme specification (e.g. for RSA, the PKCS#1 standard - see the OS2IP conversion function). In RSA, the byte string is read as a big endian number in base 256. For example, the byte string 0x01 0x02 is interpreted as the number 258 (256 * 1 + 2).