Our Sages state, “Anyone who works on Tish’a B’Av will never see a sign of blessing” from it (Ta’anit 30b). The reason is that [doing work] distracts one from mourning. However, Chazal did not prohibit work on Tish’a B’Av explicitly. Rather, some places had a custom to forbid it, while others had a custom to permit it. Thus, the Rabbis said that the local custom obligates [each individual]. Therefore, one is forbidden to work on Tish’a B’Av in a place where the custom is to refrain from doing work (Pesachim 54b). Nowadays, all of Israel has a custom to refrain from doing work on Tish’a B’Av until midday. It is proper to continue doing so after midday, as well, in order to remain focused on the mourning. Therefore, we work after midday only if it is very necessary (see Sh.A. and Rama 554:22, 24; M.B. 49).
The types of work that are forbidden on Tish’a B’Av are those that take time to perform and occupy one’s thoughts, like sewing, mending clothing, repairing furniture, fixing electrical appliances, and commerce. However, tasks that take little time to complete, like lighting or extinguishing [a candle], tying or untying, and traveling for a necessary purpose, are permitted, because they do not distract one’s mind from mourning.
Writing is forbidden, because it is a distraction, but one may transcribe things that are related to Tish’a B’Av.
It is permissible to sell food items [on Tish’a B’Av], so that people can have what they need for the meal after the fast. Starting midday, one may prepare for that meal. Some women have a custom to toil and clean the house after midday, in anticipation of Mashiach, who is [supposed to be] born on Tish’a B’Av. One should not denounce their actions (Birkei Yosef 559:7).
A Jew may instruct a non-Jew to do work for him on Tish’a B’Av. However, jobs that are done out in the open, like building a house or doing business in a store, are forbidden, because it looks like [the one who commissioned the work] is belittling the communal mourning (M.B. 554:46).
One may perform a task on Tish’a B’Av if delaying it will cause significant [monetary] loss, similar to the law on Chol HaMo’ed (Sh.A. 554:23).