The IAU website provides reliable information about philatelic correspondence with the base. There are two ways you can get your covers down there. One is through the Uruguayan Antarctic Institue in Montevideo:
Base Científica Antártica Artigas Av. 8 de Octubre 2958 CP 11600 Montevideo URUGUAY
Covers sent through Uruguay must be received by the IAU in time to be sent down to the base by ship. You can also get your covers to the base by sending mail via Chile's Frei base:
Base Científica Antártica Artigas c/o Oficina Postal Base Presidente Eduardo Frei via FACH Punta Arenas CHILE
Just as you have two options to get your covers to the base, you have the same options to get them home. Just ask the station leader (or whoever opens the mail) to send it back to you through either Uruguayan or Chilean post. Just be sure to put the correct postage on your cover, for the corresponding country. You can find the Uruguayan postal rates here I found it took much longer to get mail back through Uruguay. Perhaps because mail had to be sent from and returned to Montevideo aboard a ship. Where as mail through Frei base and Punta Areans would likely be carried by plane. The IAU website also seems to imply that mail can reach the base through the Argentine base Jubany but I have never attempted this route.
Additional information about polar philately and other stamp-related topics can be found in my Blog
last updated 30 March 2014