I'm an undergrad and will be submitting a paper to a conference soon, but it will not be reviewed until after grad school admissions are due. Should I and how would I note this on my resume?
There are similar questions to this but none are in context of grad school admissions as well as not yet accepted papers.
Yes, you should list it. It's standard practice in academia to list submitted papers on a resume or CV, and graduate applications are no exception.
Your CV should have a section for Publications. For a paper which is submitted but not accepted, you just provide the authors, title, and the word "Submitted."
M. Howard, L. Fine, J. Howard. On a novel experiment in plumbing. Submitted.
In particular, you normally do not list the name of the conference where you submitted. (If it gets accepted, then you do list the name of the conference, and replace "Submitted" by "Accepted". After it is published, you include the name of the conference and the volume and page number in the proceedings.)
If the conference allows you to post a public preprint, you should do so. And if the grad school lets you submit a writing sample or something similar, the paper would be a good choice.
However, more importantly, if this grad school requires letters of recommendation, make sure one of your recommenders discusses the paper. The mere fact that the paper was submitted doesn't give any evidence that the paper is any good. So that is where your recommender comes in. If you had a faculty mentor or collaborator on the paper, they would be a great person to ask for a letter. If it was a solo effort, then try to find someone who knows you and who is an expert in the field who can evaluate the paper's quality.
