You don't have to wait for a personal introduction to begin networking, however. Concentrate on meeting the broadest range of people you can. Then, once you've explored the organizations and contacts available to you, narrow your networking activities to those that serve you best. I thought of my embassy as the place to go if I were in trouble or had my passport stolen. It is also a storehouse of information.
Most large cities have active expatriate organizations.
For example, the British, Australians, South Africans, Scandinavians, French, Germans, and Americans all have active expatriate organizations in Madrid that meet regularly. These groups frequently advertise their meeting dates and times in free publications distributed in subway and bus stations, commercial centers, and at embassies. Don't assume that expatriate groups are self-limiting. The American Club has many members from other countries, as does the American Women's Club. The British Ladies' Society and the British Society and International Club are open to all English-speakers, whatever their nationality.