If you live in an apartment building or are renting, be sure to check with the building manager (or ‘encargado’) or your landlord to see if, first of all, they arrange for any services that you may need completed, and secondly, if not, if they have any recommendations. Often they will have handymen or companies that they utilize frequently. If you are on your own, however, your best bet for English-speaking service is the classifieds of one of the following papers or websites.
Plomeros Capital lists plumbers by barrio thoughout Buenos Aires. It has an introduction page in English but the listings are in Spanish, with no indication that the plumbers listed actually speak English.
The Buenos Aires Herald will sometimes have classifieds for services such as plumbing, handymen, etc. who speak English. Pick up the Sunday edition, as it has the most listings for the week.
Craigslist will also have listings under “Skilled Trade” for tradesmen who speak English.
BA Insider will sometimes have blogs listing recommended servicemen or tradesmen.
Buenos Aires Expats also has forums for asking and getting recommendations on skilled trade workers from other expats, as well as a sizeable archive database for searching.