After Pesaĥ, it is best not to use the ĥametz that was sold until one can assume that the rabbi has bought it all back. When necessary, though, one may take out some ĥametz immediately after Pesaĥ with a willingness to pay the gentile for it were he to request this. It is best that the beit din make an explicit condition with the gentile that the Jew will be obligated to pay for any sold ĥametz he takes, if the gentile so desires. Thus, there will be no question about the Jew taking ĥametz immediately after Pesaĥ (see Sidur Pesaĥ Ke-hilkhato 11:22).
Some people are strict and do not eat ĥametz that was sold because, according to stringent poskim, such a sale is not legitimate and this ĥametz has the status of ĥametz she-avar alav ha-Pesaĥ, which one may neither eat nor derive benefit from.
In practice, however, one need not be concerned about complying with this stringency, because the prohibition of ĥametz she-avar alav ha-Pesaĥ is rabbinic, and whenever there is uncertainty about a rabbinic law, halakha follows the lenient opinion. This is all the more true where only a small number of poskim are strict, while the overwhelming majority permit. Indeed, there were great rabbis who, after Pesaĥ, would make a point of eating ĥametz that had been sold through mekhirat ĥametz, in order to demonstrate that the sale was done in keeping with halakha.
When shopping for food after Pesaĥ, one must make sure that the seller has a certificate verifying that he sold his ĥametz in keeping with the halakha so that one does not buy ĥametz she-avar alav ha-Pesaĥ. Even more caution is needed if the seller is not religious, because if he did not understand the significance of the sale and continued to sell ĥametz in his store during Pesaĥ, a few poskim (Sde Ĥemed, Maharam Schick) maintain that the sale was not legitimate, and that it is forbidden to eat or derive benefit from any ĥametz in his store. In this case, one must preferably follow the stringent poskim and wait for goods produced after Pesaĥ to arrive. If, however, it is clear that the seller performed bedikat ĥametz in keeping with the halakha, and was careful not to let anybody go near the ĥametz that was sold, it is permissible to buy ĥametz from him as soon as Pesaĥ has ended (Sidur Pesaĥ Ke-hilkhato 11:13, 23).