As far as I know, the process is exactly the same as when you first put it up and should be done promptly. The only discussion surrounds whether a new blessing is recited. Pitchei Teshuva (YD 289:1) compares the case to one whose Tallit fell off unexpectedly who needs to recite a new blessing upon redonning it (Shulchan Aruch OC 8:14). The Aruch HaShulchan (YD 289:4) rules this way as well, as does the Kitzur Shulchan Aruch (11:7) and Mishneh Halachot (7:186). However, Rav Ovadiah Yosef (Yabia Omer OC 3:17:11) distinguishes the cases because by the Tallit, the obligation to wear Tzitzit vanishes as soon as one stops wearing the piece of clothing. On the other hand, the obligation to have a Mezuzah on the door remains in place even after the Mezuzah itself fell. Accordingly, he rules not to recite a new blessing. CYLOR for a final ruling.