The prohibitions of Shabbat include restrictions not only on our conduct and activity during Shabbat, but with regard to our speech, as well. The Shulchan Aruch discusses the laws of forbidden speech on Shabbat in Siman 306.
Among the laws in this category is the prohibition against instructing one's fellow to come to him after Shabbat for the purpose of hiring him. This invitation constitutes weekday matters and is forbidden on Shabbat. One may, however, ask rather than command another person to come to him after Shabbat for employment purposes. So long as one merely makes a request, rather than instruct or command, he may invite another person to come after Shabbat to inquire about a position.
One interesting question addressed by the Rashba (rabbinic leader of Spanish Jewry, 1235-1310) concerns announcing lost items on Shabbat, particularly when dealing with items that are Muktze (forbidden to be handled on Shabbat). Consider, for example, a case of a costly electronic device, such as a cellular phone, that was discovered in the synagogue on Friday. May the Rabbi announce in the synagogue on Shabbat that a cellular phone was found, in the hope that the owner could then retrieve it after Shabbat? Do we consider such an announcement forbidden speech, since it relates to an item that one may not handle on Shabbat?
The Rashba rules that one may announce the discovery of a lost Muktze item on Shabbat. Halacha permits speaking about weekday-related matters that involve a Mitzvah. Since Hashavat Aveda (returning a lost object) is a Mitzvah, one may announce the discovery of a lost item, even if the laws of Shabbat prohibit handling it until after Shabbat.
Summary: One may not tell another person to come after Shabbat to perform a job, but he may invite him in the form of a question (e.g. "Can you come after Shabbat?"). It is permissible to publicly announce the discovery of a lost item on Shabbat, even an item that is a Muktze, since this announcement fulfills the Mitzvah of returning lost items, and one may speak of weekday matters on Shabbat for Mitzvah purposes.
