If your city has a historical or Museum, go up there, to find out where excavations have been carried out. Archaeological expeditions can organize a historical faculties of some universities. Of course, the modest museums of regional centers are likely to conduct excavations anywhere in the place.
If you want to work on the excavation of major historical monument, look for the opportunity in the Internet. Go to the website archaeology.ru and click on "Archaeological expedition", then select the country to which you would like to get. However, it should be borne in mind that a person without experience in expeditions is unlikely to take abroad even as a laborer. It would be wise to choose the tab "CIS". You will see records of old expeditions and invitations to work in new.
Most likely, you will be asked to work for free. You pay only for travel to site and meals. Even in these conditions wanting to work in the expedition is more than vacancies, so preference is given to candidates that have beneficial in the field speciality: geologists, surveyors, architects, artists, restorers, cooks, doctors.
Many expeditions are financed by sponsors, including its members. In this case you will have to pay not only the ticket to the place of excavation, and nutrition while working. To find such offers in the Internet, type "archeological expedition" in Google search.
The Crimean Peninsula is famous for archaeological excavations. You can go to the Museum of Chersonesos reserve, which is located in Sevastopol, by phone +38 (0692) 55-02-78, 24-13-69, 24-14-15, in the summer to go on an archeological expedition. Similar services are provided and the Bakhchsarai state historical and archaeological reserve. His phones: +38 (06554) 4-74-81, 4-28-81)