Gemara

39a - Rav Yehudah: We bless on all Mitzvos before doing them.

41b (Mishnah - R. Yosi): If the first day of Sukos was on Shabbos and someone took a Lulav into Reshus ha'Rabim he is exempt, for he had permission.

42a - Abaye: He is exempt if he was not Yotzei (he was obsessed with the Mitzvah), but if he was Yotzei he is liable.

Question: The moment he picked it up he was Yotzei!

Answer #1 (Abaye): It was upside down.

Answer #2 (Rava): It was in a Keli.

45b - Chizkiyah: One is Yotzei Mitzvos only the way they grew - "Atzei Shitim Omdim".

Pesachim 7b: Rav Papi holds that 'Al' connotes past tense.

Question (Beraisa): One who makes a Lulav (ties the Hadasim and Aravos to it) blesses Shehecheyanu. When he takes it to be Yotzei, he blesses 'v'Tzivanu Al Netilas Lulav'.

Answer: There the past tense is appropriate, for he was already Yotzei the moment he picked them up!

Question: If so, why does it say 'when he takes it to be Yotzei?' It should say, after he fulfilled the Mitzvah!

Answer: Indeed, it should say this. It says 'to be Yotzei' for consistency with the Seifa:

(Seifa): One who makes a Sukah for himself blesses Shehecheyanu. When he enters to dwell in it, he blesses 'v'Tzivanu Leshev ba'Sukah'.

Menachos 35b - Rav Shmuel bar Bidri: We bless on Tefilin (Shel Yad) after putting them on.

Question: Rav Yehudah taught that we always bless on a Mitzvah before doing the Mitzvah!

Answer (Abaye and Rava): He means, after putting it on and before tying it (tying is the completion of the Mitzvah).

Rishonim

The Rif (20a) and Rosh (3:32) bring the Gemara.

Ran (DH umid'Parchinan): Some say that one must bless on the four Minim before picking them up, for we must bless before the Mitzvah, and once he picks them up he is Yotzei. This is wrong. One blesses on Tefilin between putting them on and tying them. We do not bless when a Mitzvah is merely prepared. Others say that we pick it up upside down until the Berachah, for one is Yotzei only the way things grow. Also this is wrong, for the Gemara (Pesachim 7b) says that we bless 'Al Netilas Lulav' (and not 'Litol', which would connote the future) because he already fulfilled the Mitzvah the moment he picked them up! Chachamim did not obligate one to pick it up upside down. Even though he is Yotzei before the Berachah, this is called blessing before the Mitzvah, for one must still shake it. However, we do not bless after finishing a Mitzvah.

Rambam (Hilchos Berachos 11:15): After taking the Lulav he blesses Al Netilas Lulav, since he was Yotzei once he picked it up. If he blesses before picking it up he blesses Litol Lulav, just like Leshev ba'Sukah. One who blesses after doing the Mitzvah blesses Al ha'Asiyah.

Rebuttal (Ra'avad): According to this, if one did not bless before putting on Talis or Tefilin he would bless 'Al Atifas Tzitzis' or 'Al Hanchas Tefilin'! This is wrong, for the Mitzvah applies the entire day. 'Al' applies to Lulav, for he is no longer obligated today, or to Bi'ur Chametz, for once he decided (to Mevatel it) in his heart Bi'ur was done.

Rambam (Hilchos Lulav 7:6): One blesses Al Netilas Lulav first, since they are all near him. Afterwards he takes the bundle in his right hand and the Esrog in his left hand. He takes them the way they grew, with the root down and the top up.

Beis Yosef (OC 651 DH u'Mah she'Chosav she'Ein): The Rambam does not say that the text of the Berachah is 'Al Netilas Lulav'. Since he says to bless beforehand, surely he blesses 'Litol'. Rather, he teaches that the Berachah mentions the Lulav, and not the other Minim. He gave the text of the Berachah in Hilchos Berachos. In Hilchos Lulav (7:15) the Rambam says that nowadays we take the Lulav and bless '...Al Netilas Lulav' every day. He comes to teach that we bless even though it is mid'Rabanan. Also there he relies on what he wrote in Hilchos Berachos regarding the text of the Berachah.

Rambam (9): Once he lifts the four Minim he is Yotzei. This is only if they were the way they grow.

Rosh (3:33): It would seem that it is better to bless before picking up the four Minim, for we bless before Mitzvos. However, it is unreasonable to bless while they are still in a Keli, before it is ready in his hands. We bless on Tefilin after putting it on and before tying it. It is good to bless after taking the Lulav, before taking the Esrog. This is before the Mitzvah, for all the Minim are Me'akev each other. Alternatively, he holds one of the Minim upside down until blessing, or has intent not to be Yotzei until blessing. Even though Mitzvos do not need intent, one is not Yotzei against his will. The Gemara did not answer that this is how one can be liable for carrying them in Reshus ha'Rabim. Since he was heading to ask someone, presumably he is not so knowledgeable to know to have negative intent. Alternatively, one may bless after picking them up normally because the Mitzvah is not finished until shaking it. Similarly, we bless on Netilas Yadayim after washing the hands, because the Mitzvah is not finished until drying them. The Gemara (Pesachim 7b) supports this. It says that one was Yotzei the moment he picked them up. It was the custom to hold the Lulav during all of prayer. Even though this is not Me'akev, since it is the ideal Mitzvah, one who blesses after picking them up is blessing before (completion of) the Mitzvah. The Yerushalmi says one who covers himself with a Talis blesses (afterwards) 'Lehis'atef ba'Tzitzis'. This is not a solid proof, for there the Mitzvah extends as long as he wears it. Here, he was already Yotzei.

Poskim

Shulchan Aruch (651:5): One blesses Al Netilas Lulav and Shehecheyanu before picking up the Esrog, in order to bless before doing the Mitzvah. Alternatively, one may hold the Esrog upside down until blessing.

Rebuttal (Gra): The Gemara (Pesachim 7b) says that one blesses even though he was already Yotzei. Holding the Esrog upside down does not help. Since all four Minim are in front of him he need not take all at once, and he is Yotzei Lulav even if he is not yet Yotzei Esrog! It is best to have intent not to be Yotzei before blessing.

Question: Why didn't the Shulchan Aruch suggest having intent not to be Yotzei before blessing?

Answer #1 (Taz 5): If so, there would be no Shinuy Ma'aseh reminding him to do so, and perhaps he will come to bless after taking them without intent.

Answer #2 (Magen Avraham 12): Some say that Mitzvos do not require intent.

Note: Perhaps he refers to the opinion of the Ro'oh (brought in Beis Yosef (589, DH Lefichach) that according to the opinion that Mitzvos do not need intent, one is Yotzei against his will. (He learns from one who was forced to eat Matzah.) However, the Beis Yosef says that we are not concerned for this minority opinion.

Answer #3 (Kaf ha'Chayim 58): Some say that not everyone knows how to have such intents. The Shulchan Aruch gives ways that anyone can fulfill, but one who knows how to have negative intent can do so.

Kaf ha'Chayim (59): Some say that it is a disgrace to hold the Esrog upside down. The custom is to bless before taking the Esrog.

Beis Yosef (ibid.): If one takes the Lulav in this way and blesses before being Yotzei, it is fitting to bless 'Litol'. The custom is always to bless 'Al', for once he picks it up he was partially Yotzei. The Rambam says to bless 'Litol' only if he did not pick it up at all yet.

Beis Yosef (DH Kosuv b'Orchos Chayim): A case occurred, R. Meshulam blessed Al Netilas Lulav and Shehecheyanu and did not find an Aravah inside. He put in an Aravah and took everything and blessed Al Netilas Aravah, and Shehecheyanu for the Mitzvah of Aravah, which he was not Yotzei the first time.

Drishah (1): Even though he was not Yotzei anything because the Minim are Me'akev each other, it was better to bless the second time on the Min he had not taken at all. The same applies if one finds that one of the Minim was upside down.

Note: This connotes that even if he realized that one was upside down before saying anything else, he must bless again. We must understand why we do not say that he was Yotzei since all the Minim are in front of him and he can take them one after the other.

Mishnah Berurah (26) and Sha'ar ha'Tziyon (31): If one did not bless before picking them up he may do so afterwards because the Mitzvah is not finished until shaking it. Poskim argue about whether or not he may bless if he already shook it.

Mishnah Berurah (41): If one obtained a Lulav in the middle of Hallel he may bless on it between one Perek of Tehilim and another.