It is clear that Abraham understood the Torah, and that he waited to enact his bris until commanded, but who performed it? Did he do it himself, or was someone else instructed to do it, to serve in the sealing of his covenant?
Pirkei D'Rebbi Eliezer 29 says that Shem Ben Noach performed Avraham's bris.
The Medrash Rabba Bereishis 49:2 says that Hashem held Avraham's hand and helped him perform the bris.
The verse in Bereishis 17:24 supports that it was performed by someone else, as it uses the passive language בהמולו, when he was circumcised, and Rashi there points out that this is הפעל, acted upon.
וְאַבְרָהָם בֶּן תִּשְׁעִים וָתֵשַׁע שָׁנָה בְּהִמֹּלוֹ בְּשַׂר עָרְלָתוֹ
This website recounts the medrash that says that
According to the Midrash (Tanchuma VaYeira 3), Abraham only circumcised himself after consulting with his friend Mamrei.
The Midrash Rabbah Lech Lacha 9: "א"ר לוי מל אברהם אין כתיב כאן אלא נימול בדק את עצמו ומצא עצמו מהול "
Reb Levi said that the Torah said nimol Avraham opposed to maol Avrham,meaning Avraham checked and saw that he had a milah already.
Avraham circumcised himself together with God.
בראשית רבה מט ב.
אמר לפניו ומי ימול אותי? אמר: אתה בעצמך. מיד נטל אברהם סכין, והיה אוחז בערלתו ובא לחתוך והיה מתירא שהיה זקן, מה עשה הקדוש ברוך הוא? שלח ידו ואחז עמו והיה אברהם חותך,
Bereshit Raba 49b
Avraham asked God "who will circumcise me"? God replied: you will. Immediately Avraham took a knife and held his foreskin, and wanted to cut it, but he was afraid because he was old. What God did do? He reached with his hand and held on togather with him, and Avraham did the cutting