Radak: She gave praise and thanks to Hashem, and prayed that Shmuel will live and be to Hashem.

Radak citing Targum Yonasan: She prayed with a spirit of prophecy, and said that Shmuel will be a Navi. Yonason explained how other verses allude to future Nochri kings, and Keneses Yisrael.

Aderes Eliyahu: This Tefilah or Mizmor is the Klal of all the miracles Hashem did and will do for us, from Avraham ¹ until Mashi'ach. It has 10 verses, corresponding to the 10 Sefiros, from above to below. All parts of the world encompass 10 matters; all the Mitzvos are revealed in Aseres ha'Dibros.

Malbim: The first nine verses are praise; the last verse (10) is the Tefilah. One first arranges Hashem's praises before praying! (Brachos 32a)

Rashi: It is Peninah. Radak - Chanah discusses how Hashem lowers the haughty and raises the humble.

Radak: (It is plural.) It is Peninah and others who angered her when she was barren.

Bi'ur ha'Gra: [Yakov ¹ overcame] Esav and Lavan.

Megilah 14a: My horn is raised, but not my flask. David and Shlomo were anointed with a horn (of oil), and their kingships lasted. Sha'ul and Yehu were anointed with flasks, and their kingships did not last.

Radak: Before, she could not raise her head in front of her co-wife. Now, she can.

Malbim: This refers to becoming pregnant. Initially, when Eli promised her, just her heart exulted.

Radak: Hashem saved her from her pain, and gave to her a son.

Bi'ur ha'Gra: (This alludes to Yosef.) You (Hashem) saved him; the Sar ha'Mashkim forgot him.

Malbim: Her Simchah is because it is Your salvation, via a miracle that shows His wondrous Hashgachah.