Generally, what you'll need is three things:
1. That your Android phone supports USB host mode (aka USB On The Go, aka USB OTG)
2. A USB OTG adaptor that plugs into your phone and typically has a full size USB socket on it. Some of these are simple cables, others may include a card reader
3. A USB serial adaptor cable that plugs into the OTG adaptor. There are lots of these around, often based on an FTDI chipset. Some come with bare ends, some terminate in a nine pin socket or plug, some in a 3.5m jack.
Plug all those things together, add the UsbSerial library, and you have a solution. Also, often, lots of things dangling out of the bottom of your phone, which is a bit of a pain, and one reason why adding a bluetooth dongle to the device you want to communicate with is often more convenient.
As Bill says above, voltage levels are very important. Some cables will be built to operate at 3.3volts, some at 5 volts, and some at higher levels - most especially older equipment with built in real RS232 ports.
The Max232 will look after level adjustments, but if you have an adaptor that works at the right levels as your device, you may not need one. And, if you're brave, you can adapt between 3.3v and 5v levels just with a couple of resistors (no warranty implied... at your own risk).