Unlike 'Dynamic' microphones all condenser microphones require some sort of power supply to make them work. Sometimes this can be by way of an internal battery but many of them work on an external 'phantom' power supply.
I am not familiar with the exact model number you quote but AT make 2 types of AT2020 condenser microphone.
1) If your AT microphone is fitted with a USB plug then you can connect it directly to the USB socket on your computer, which will provide it with the power that it needs to make it work.
The USB bus should automatically recognise the microphone and allocate an audio channel to it but you may still have to select this device as your input source in your recording program. How you do this will differ from one program to another.
2) However if the microphone is fitted with a standard jack-plug then it will not work by you just plugging it into your computer microphone input socket as this is not powered. You will need a separate 48volt DC power supply to power the microphone.
You will almost certainly also need some sort of microphone pre-amplifier to match the output voltage and impedance (electrical resistance) of the microphone to the levels required by your audio input socket on your computer.
Probably the best way to achieve both of these requirements at lowest cost would be to purchase a small audio mixer with a phantom power option such as the Phonic AM220 http://cpc.farnell.com/phonic/am220/mixing-console-am220/dp/DP29303
- most audio mixers only have one on/off switch for phantom, power - thus the power is either on or off for ALL channels. Some other devices - like radio microphones, keyboards and electric guitars may be damaged by having 48v dc current supplied to them
Here is a link to the technical specs sheet for the AT2020 http://www.audio-technica.com/cms/resource_library/literature/49f63e6efc082082/at2020_english.pdf
More information is available here http://www.dolphinmusic.co.uk/article/40-why-do-i-need-a-microphone-preamp-.html