The owner of a grocery store must open up on Ḥol Ha-mo’ed to provide his customers with food for the festival. Since it is clear that this serves a festival need, he need not be discreet about it. He may also record his sales and provide receipts, as required by law (SA 539:10).
At first glance it would seem that the store owner may not sell anything to a non-Jew, since the basis for permitting him to open during Ḥol Ha-mo’ed is to provide food for the festival. Since a non-Jew has no mitzva to rejoice on the festival, it should be forbidden to sell to him. In practice, though, once it is permissible for the owner to open his store to sell Jews food for the festival, he may sell to non-Jews as well, for the sake of maintaining good relations (mipnei darkhei shalom) (MB 539:33; see Harḥavot). Similarly, it would seem, at first glance, to be forbidden to sell something to a non-observant Jew, who might be buying what he will need after the festival. In practice, however, there is no need to clarify the purpose of his purchases, and so it is permissible to sell to any Jew.
All this applies to food stores, but the general practice is that other stores do not open on Ḥol Ha-mo’ed. Even though it is permissible to buy clothing, shoes, utensils, and electrical appliances for the festival (MK 13a-b), this is only when they are truly necessary. For example, if a woman’s Yom Tov dress tore or got dirty and she needs a new one to wear on the last day or days, she may buy it on Ḥol Ha-mo’ed. However, when the item is not absolutely necessary, but would just be nice to have, she may not buy it on Ḥol Ha-mo’ed. For example, if a woman has a Yom Tov dress, but she’d like to buy another one which she likes better, she may not do so on Ḥol Ha-mo’ed. Furthermore, even if it is truly necessary for the festival, but she could have bought it before Yom Tov and neglected to do so, she may not buy it on Ḥol Ha-mo’ed, since it is as if she planned to do melakha on Ḥol Ha-mo’ed.
In practice, the widely accepted custom is to make sure to buy everything one will need for the festival beforehand. If stores were to open on Ḥol Ha-mo’ed, most of the customers would either be buying items unnecessary for the festival or items they had neglected to buy beforehand. It is forbidden to open a store for them.
If one needs clothing or shoes urgently, and was not negligent before the festival, he may call a store owner and ask to purchase the necessary item on Ḥol Ha-mo’ed. If a store owner knows that every day there will be some Jews who need to buy what he sells for the festival (and whose need is not due to negligence), he may open his store for a few hours each day. However, he must be careful to sell discreetly. If the store is located in an out-of-the-way place, he may open it normally. If it is on a typical street, he should open it a bit differently than usual. For example, if the store has two doors and he normally leaves both open, he should open only one; if the store has one door and a security grating, he should leave the grating halfway down. This way, it will be clear that he is not doing business as usual. He should also put a note on the door that says: “This store is open for festival needs between the following hours” (SA 539:11). Even when it is permissible to buy something on Ḥol Ha-mo’ed, it may not be bought at a store that is not allowed to be open (see 11:16 above).