I overstayed my 90-day visa by roughly 23 days in September 2013. I desperately want to return to the US for a week. Am I eligible to enter us again, as it has been 3 years? Does my ban come into effect when I left or does it start when I try to re-enter? If I am allowed to re-enter, would I just apply via ESTA.
When you say you overstayed "my 90 day visa", do you by any chance mean that you were admitted for 90 days without having a visa, under the Visa Waiver Program?
If so, having overstayed once makes you forever ineligible to use the VWP again, pursuant to 8 U.S.C. 1187(a)(7).
You can apply for a B-1/B-2 visa for your trip, but during the application you will have to disclose that you have a previous overstay (otherwise it's visa fraud which will earn you a ban), so you'd better have a good and convincing story ready about why you overstayed and how they can be sure you won't do so again.
If you entered on an actual visa before overstaying, then it doesn't look like a 23-day overstay will make you inadmissible, so in principle you can just apply for an ESTA in that case.
Be sure to answer "yes" to the "Have you ever stayed in the United States longer than the admission period granted to you by the U.S. government?" question on the ESTA form -- lying there will get you in considerably hotter water than the overstay itself will. It wouldn't surprise me if the ESTA is rejected on this ground (though I cannot find any source that outright says it must), so apply sufficiently long time in advance that you have time to apply for a visa if that happens.