If you feel you have written a significant piece of academic work as an undergraduate, consider submitting it for publication to a scholarly journal. Some journals cater to undergraduate writing in particular. Beginning to build a list of relevant scholarly publications, as well as presenting papers at conferences, will be a terrific asset to your graduate school application.
Start by talking with faculty. Ask the professor for whom you wrote the paper if s/he believes it is ready to be submitted for publication. Ask for ideas and for guidance.
Read scholarly journals in your area(s) of interest. The English Subject Pages for the UW Libraries contain directories for finding publications in specific subfields. You can also look at faculty profiles for professors (at the UW and elsewhere) working in research areas that are similar to yours and read the articles they have written.
Explore journals that feature undergraduate work. A list of publications, at the UW and beyond the UW, can be found on the UW Undergraduate Research Program's website. The Council on Undergraduate Research also features an extensive list of undergraduate journals.
Watch notices of calls for papers (CFPs). These are sometimes sent to students through the englmajors e-mail list when they are targeted directly at undergraduates. The American Comparative Literature Association (ACLA) maintains a listing of calls for papers, as do the University of Pennsylvania English Department (subcategory menus on the left side) and the Modern Language Association (MLA). The Voice of the Shuttle maintains an extensive list of CFPs and conferences.
Use the UW Libraries Publication Guide for the Humanities, developed by English Studies Librarian Faye Christenberry. This guide includes an overview, suggestions for finding a journal and evaluating its impact, a list of publishing directories, and more.
For examples of undergraduate research leading to publication and conference participation, see the English Department's Undergraduate Research page.