The Arizal (Sha’ar HaKavanot 50b) writes that when one bows in Alenu Leshabe’ah, namely when saying “VaAnahnu Mishtahavim”, one is enveloped by a protective spiritual light. Practically speaking, the Ben Ish Hai (Od Yosef Hai, Ki Tisa, § 21) explains that the bowing should be done in one movement, rather than bending one’s knees and then bowing.
The second paragraph of Alenu Leshabe’ah begins with the words “Al Ken Nekave”, whose initials Rabbi Moshe ben Machir (Seder HaYom) explains spell out the name “Achan”. Achan was among the men who helped Yehoshua conquer Jericho, but he partook in the spoils of war which Yehoshua had consecrated to Hashem. Achan was eventually executed for his sin, but first repented. As such, the Seder Hayom and Rabbi Natan Spira (Mehale Amukot, Va’ethanan) both explain that Achan composed this paragraph and it was included in Alenu Leshabe’ah. The Maharal (Be’er HaGola) and Rabbi Yair Bachrach (Mekor Haim § 132) object to the idea that our Sages would have included a prayer from Achan, and that the actual composer was Yehoshua.
Summary: One should bow in one movement when saying “VaAnahnu Mishtahavim”. One should recite “Al Ken Nekave” with concentration.