What is "No'am Hashem"?
Rashi: His Shechinah and consolations.
Radak: This verse applies to the days of salvation. Then, the work of our hands will be proper - "Lo Yig'u la'Rik v'Lo Yeledu la'Behalah" (Yeshayah 65:23).
Malbim: No'am is the pleasure that a worker gets from his action, when he gets the desired result. Via attaining perfection, Hashem will find pleasure in the creation that He created for His honor. The creations will fathom His honor and serve Him, and this will be seen on us, for we will be the purpose of the creation and Hashem's desire in His world.
What is the meaning of "u'Ma'ase Yadeinu Konenah Aleinu"?
Rashi: This is a request (establish the work of our hands). Konenah is like "Shamrah", "Shaftah" (25:20, 82:8).
Malbim: The work of man's hands in lowly matters is not established on him. It is not a basis for his deeds. E.g. if one builds a house to live in it, the house is founded on a foundation of rocks, and the rocks are founded on earth of the ground, and not on the builder. Just the contrary - the builder intends to dwell in the house and take refuge from floods and rain. Spiritual matters are different. [The builder] becomes a foundation for his acts. E.g. one who learns Torah, his Torah is founded on his intellect and Nefesh. One who does a Mitzvah Lishmah, the Mitzvah has a base in his Nefesh. Moshe requests that our actions be founded on us, and not something external to us. Hashem should establish all that we do, for it should be good in His eyes. Moshe's Tefilah was for the Klal, and also for himself; he did not understand the decree that he not enter Eretz Yisrael. He wanted to enter the land to see Hashem's actions, and attain his perfection.
Why does it repeat "u'Ma'ase Yadeinu Konenehu"?
Rashi: One applies to building the Mishkan; Moshe blessed Yisrael, and prayed that the Shechinah will dwell in the work of their hands, i.e. the Mishkan. The other is that there should be Brachah on the work of their hands.
Radak: This is to strengthen the matter.
Malbim: Moshe asked this his action, of taking Am Hashem out of Egypt, be founded on him, and not on another.