This seems to be quite a common problem, and there are a number of problems, each with their own solution.
- Make sure you have selected the right chip
- Make sure you have selected the right serial port (when you unplug your board, it should disappear).
- Make sure you do not have anything plugged in to the tx & rx pins (usually 0 and 1).
- Make sure your Atmega chip has a bootloader on it
- Try another cable
- There may be a problem with your computer - try another computer
- If using another helps, try reinstalling the USB serial driver
- Try unplugging the Arduino board, holding down the reset switch, then plugging it in (still holding down reset); continue to hold down reset for about 5 seconds.
- make sure nothing else is trying to use your serial port
- Does your chip have a bootloader? Chips bought as part of an Arduino will, otherwise, it almost certainly doesn't, unless it specifically says (in the description of what you bought).
If it does not have a bootloader (or may not have a bootloader) you will need to set this up. You can either use the instructions here: https://www.arduino.cc/en/Tutorial/ArduinoToBreadboard (which I never got working) or you can use an ICSP like the http://www.freetronics.com.au/products/usbasp-icsp-programmer-for-avr-arduino#.VlIY_2xifXs (which is what I use) - works great. They can be had for a few dollars from China.