The basic halacha is that this is normally muktza (because of Nolad) and should not be brought in on Shabbos. If the nonJew puts it down in your house, you should leave it until after Shabbos to open it.
Handling Mail Received on Shabbat
Is it permissible to open mail or packages that were delivered to one's home on Shabbat?
Rav Shemuel Pinhasi (contemporary), in his work DaberVeDaber Davar (p. 111), rules that if mail was delivered to the mailbox outside the door to one's home, he should Le’chatchila not bring it into his home until after Shabbat. If the mail was delivered into his home, it is forbidden to open any letters or packages. In fact, it appears from a comment of the Peri Hadash (commentary to the Shulhan Aruch by Rav Hizkiya Da Silva, 1659-1698), in Yoreh De'a (118), that opening letters or packages on Shabbat constitutes a Torah violation. Although many other authorities dispute this position, all agree that this is forbidden on Shabbat, at least on the level of Rabbinic enactment.
Nevertheless, Rav Pinhasi rules (listen to audio recording for precise citation) that one may ask a gentile to open a letter or package for him on Shabbat, provided that he expresses his request in the form of a "Remez" (a subtle allusion). He might say, for example, "I would like to read this letter but it's closed." Once the non-Jew opens the package, it is permissible to make use of the items. Even though the letter or package had been brought from outside the "Tehum" (area beyond which one may not travel on Shabbat), Halacha nevertheless allows one to handle these items on Shabbat.
Of course, this assumes that the material he would like to read is permissible and appropriate for Shabbat, such as Torah educational journals and the like. Furthermore, Rav Pinhasi notes, one must ensure that the envelope or package does not contain any Mukseh items. But assuming the items are not Mukseh, one may indirectly ask a non-Jew to open the package on his behalf on Shabbat. Thus, for example, if a person received food items or jewelry in the mail on Shabbat, and he would like to use the product on Shabbat, he may allude to his non-Jewish housekeeper that he wishes her to open the package for him.
Summary: Mail delivered to an outdoor mailbox should not be brought inside the home on Shabbat. If the mail was brought inside the home, one may not open the envelope of package, but he may hint a request to a non-Jew to open it for him, assuming, of course, that the contents are not Mukseh or otherwise inappropriate for Shabbat.