How did Chana vow that her son (Shmuel hanavi) should be a Nazir, when the (Gemara Sotah 23a) says a woman can't impose Nezirut on her son?
Numerous answers are suggested for this question discussed as early as the Rishonim (cf. Radak here).
R. Moshe Zacuto (notes to mishnah Naz. 9:5) understands that Chana didn’t impose a Nazir vow rather she intended to groom the boy as a parush (to abstain from wine etc.) and when the boy would become of age he’d hopefully accept Nazirut by himself.
Others suggest that Chana intended that shed implore her husband, Elkanah, to uphold/articulate the vow (don’t recall source at the moment - feel free to revise).
The Bais Halevi http://www.hebrewbooks.org/rambam.aspx?mfid=13316&rid=5763 * quotes the Radak asking this very question of how could Shmuel's mother make her son a Nazir:
הרד"ק הקשה דאיך חל עליו הנזירות דהא קיי"ל אין אשה מדרת בנה בנזיר
He answers that Shmuel Accepted the Nezirus on himself again when he was old enough (so when he killed Agag he was able to shoel Chacham on his own Nezirus inorder not to transgress becoming Tamei)
וראיתי מי שתירץ דאח"כ כשהגדיל קיבל עליו הנזירות בעצמו וכיון דהוי נזיר מפי עצמו שפיר מועיל שאלה
*Rav Yosher Ber Soloveitchik Rav of Brisk 19th century great grandfather of the "Rav" Yosher Ber Soloveitchik