Each morning, one is required to recite Birkot Ha'Torah before he learns Torah for the first time, and this recitation covers all his learning throughout the day and the following night, until the next morning. However, the Poskim debate the question of whether sleeping ends the "coverage" of Birkot Ha'Torah, such that one must recite Birkot Ha'Torah again once he wakes up before he learns Torah. The Shulhan Aruch observes the widespread custom not to repeat Birkot Ha'Torah after waking from a nap during the day, though the Mishna Berura cites numerous later Poskim who rule that one must, indeed, repeat Birkot Ha'Torah in such a case.
In light of the different opinions, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes (in Parashat Vayesheb) that after taking a nap, one should preferably recite Birkot Ha'Torah but omit the words "Hashem Elokenu Melech Ha'olam." He should silently think these words in his mind, without articulating them, and then complete the Beracha. The Kaf Ha'haim (Rav Yaakob Haim Sofer, Baghdad-Jerusalem, 1870-1939) recommends having specific intent when reciting Birkot Ha'Torah in the morning that it should cover his Torah learning even after he sleeps during the day. This intention may be effective in obviating the need to repeat Birkot Ha'Torah according to all opinions.
This applies only in the case of a person who takes a nap during the day. A nap taken after dark, however, indeed ends the effect of that morning's Birkot Ha'Torah. Thus, for example, if a person comes home from work after dark, and then takes a nap before attending a Torah class, he must recite Birkot Ha'Torah upon waking, before attending the class. This applies only if the person went to take a nap in his bed or on the couch, but not if he dozed off on the bus or at the table. Additionally, this Halacha applies only after what the Poskim call a "Shinat Keba" – a real nap, as opposed to a quick doze. Hacham Ovadia Yosef maintained that even two minutes of sleep qualifies as "Shinat Keba," whereas Hacham Ben Sion Abba Shaul (Jerusalem, 1924-1998) held that a nap of 30 minutes or longer is needed to require the recitation of Birkot Ha'Torah after waking. Hacham Ben Sion added that if a person went to sleep around 15 minutes before sundown, and slept for a half-hour, he must recite Birkot Ha'Torah upon waking, even though he slept less than 30 minutes in the evening.
Another important condition to this Halacha is that the person had already recited Arbit before taking a nap. If a person took a nap in the evening before he recited Arbit, then he does not repeat Birkot Ha'Torah afterward, and he should instead have in mind to fulfill his Birkot Ha'Torah obligation through the recitation of the Beracha of Ahabat Olam during Arbit.
As mentioned, one's recitation of Birkot Ha'Torah in the morning covers all his Torah learning through that entire day and that night, until the next morning. The Poskim therefore advise that if somebody remains awake throughout the night – such as on the night of Shabuot – he should not recite Birkot Ha'shahar (the morning blessings) until morning. Although the other morning blessings may be recited already from Hasot (halachic midnight), Birkot Ha'Torah should not be recited until morning. If a person recites Birkot Ha'shahar before morning, he might mistakenly recite Birkot Ha'Torah, which he normally recites together with the other morning blessings. It is therefore advisable when remaining awake throughout the night not to recite Birkot Ha'shahar until dawn, when he can recite even Birkot Ha'Torah.
Summary: Some Poskim require one to repeat Birkot Ha'Torah after taking a nap during the day, before he learns Torah, though the accepted practice does not follow this view. Some Poskim advise reciting Birkot Ha'Torah upon waking without the phrase "Hashem Elokenu Melech Ha'olam," and to think these words silently in one's mind without articulating them. This applies only if one took a nap during the day. If one took a nap after dark, in his bed or on a couch (as opposed to dozing on the bus or at the table), and he had already recited Arbit, then he must recite Birkot Ha'Torah after his nap, before he learns Torah. If he had yet to recite Arbit, then he does not recite Birkot Ha'Torah after his nap, and instead should have in mind to fulfill his Birkot Ha'Torah obligation through the recitation of the Beracha of Ahabat Olam during Arbit.