What is the purpose of the writing? Is it a school assignment?
Every year, since I could remember, I have made New Years resolutions that usually last about a week.
Here's a couple of grammar points. The first comma isn't needed. The sentence is a little awkward. Do you mean every year since you had the capability to remember? Every year? Recent years? Nail it down. An apostrophe is needed in New Year's. The resolutions belong to the New Year. Think of it like saying, "Tuesday's to-do list" versus "I always to AA on Tuesdays."