I bought a cheap Chinese Arduino Mega 2560 clone and had some major problems (I had to google it and it was not the first link!). The main problem is that the cheap one uses CH340G or CH341G as the USB/Serial chip instead of the FTDI chip. First check that you have a USB data cable, not just a power cable.
avrdude: ser_open(): can't open device "/dev/tty*": Resource busy ioctl("TIOCMGET"): Inappropriate ioctl for device avrdude: ser_send(): write error: Bad file descriptor Problem uploading to board. See http://www.arduino.cc/en/Guide/Troubleshooting#upload for suggestions.
To fix the problem install the drivers for the chip instructions here!