If you use the MAX232, the voltage swings will be bipolar with positive & negative voltages on the TX & RX lines. Respectively, if using RS232 levels, you must interface the other side of the wiring with another RS232 transceiver (TX & RX). The transceiver (MAX232 or equivalent) will take your CPU CMOS levels (often CMOS levels are @ 3v3) and shift to +5 / -5V. Typically, these days, RS232 transceivers are operating @ 3v3 but they feature a capacitor voltage doubler for the I/O. So this translates to about +6 / -6 volt swings on the RS232 pins.
You CANNOT safely interface RS232 directly to CMOS pins on the CPU. Again, RS232 to RS232 transceivers must be used. With RS232 transceivers you can drive the cable longer than if you do NOT use RS232 transceivers. Varying directly with the baud rate (speed of the serial port) and the quality of your RS232 wiring, you can run say 20-50ft with 9600bps / 19200bps. There are many articles on this topic but if you must run very long cables then consider RS422 or RS485 transceivers instead. With the differential signals of RS422 / RS485 transceivers, you can run upto 4000ft at the slower baud rates.
MAX232 is an old school transceiver but a stable one. Consider devices with 15kv ESD protection to protect against carpet zaps, etc. - static does KILL the parts.