Eventually something will be in need of repair, and determining who the right handyman for the job might be, and how best to contact them, can be a bit complicated.
If you live in an apartment and have problems with the electricity, gas, or water, or for equipment that came with the house (washer/dryer, dishwasher, air conditioning, etc.) it’s usually best to contact your building manager to ask for their support. Most expat apartments come with 12 to 24 hour on-site building management staff that can address many issues. Alternatively, you can contact your real estate agent who can then connect you (or help broker communications) with a repairman.
Chez Vous (http://www.chezvous.co.jp/english/) is a foreigner friendly handyman service that can help with a variety of needs including minor air conditioning maintenance, carpet cleaning, audio visual equipment setup, do it yourself assembly, etc.
If it’s something that you purchased yourself (i.e. it didn’t already exist when you moved it), it’s best to either call or return to the store where you originally purchased the item. Many stores work with licensed repairmen that can come directly to your home, and by and large they are inexpensive and can speak some limited English.
Several free English language magazines and websites can also help with your search: http://www.japantoday.com, http://www.tokyonoticeboard.co.jp/, and http://metropolis.co.jp.