It is customary among Sepharadim to recite Selihot each morning during the month of Elul, ideally around the time of dawn. One should recite the morning Berachot before reciting Selihot; in particular, one must ensure to wash his hands with the Beracha of "Al Netilat Yadayim," and recite Birkat Ha’Torah, before Selihot.
It should be noted that according to some authorities, the time for the morning hand washing begins only at dawn. We do not follow this opinion, as we allow a person to wash his hands with the Beracha as soon as he wakes up with the intent of remaining awake for the day, even if this occurs in the middle of the night. However, in deference to the view that the time for washing begins only after dawn, one who washed his hands before dawn should preferably wash his hands again – though without a Beracha – after dawn. During the period of Selihot, then, one should arise early, wash his hands with a Beracha, recite the other morning Berachot, and then recite Selihot. After Selihot, he should preferably wash his hands again without a Beracha.
As mentioned, the preferred time for reciting Selihot is the time of dawn, as this is the time when the Almighty is especially receptive to our prayers. Nevertheless, it is permissible to recite Selihot earlier, anytime after Hasot (midnight as defined by Halacha), or later, anytime throughout the day. Thus, for example, many communities hold Selihot services late on Mosa’eh Shabbat, after Hasot, since many people are up late on Mosa’eh Shabbat and it would be difficult for them to wake up at dawn for Selihot. By the same token, people who, for whatever reason, cannot recite Selihot early in the morning may arrange a Minyan for Selihot at any point throughout the day.
Summary: Selihot should ideally be recited at dawn, though it may be recited at anytime from Hasot (midnight as defined by Halacha) until the end of the day. One should perform the morning hand washing with a Beracha and recite the other morning Berachot before reciting Selihot. If one washed his hands before dawn, he should preferably wash his hands again after dawn without a Beracha.