Funding for your project will most likely come from a grant from the Principal Investigator of your lab. However, that doesn't mean that you can't find other ways to fund your project.
One of the most well-known research awards on campus is the Undergraduate Teaching and Research Award for which you can apply for funds during the school year or the summer. The UTRA is a salary support for research. Students at Brown (as at most schools) cannot earn both course credit and wages or stipends for the same research hours.
Another source of funding through Brown is the Research at Brown Grant (RAB) which allows you to submit proposals for assistance of up to $500 (not a salary support). With these funds you can purchase necessary equipment or receive reimbursement for costs of travel to a research site or conference.
There are a few places outside of Brown that allocate grants to undergraduate researchers. Most notably, the Sigma Xi Research Society awards Grants-In-Aid of Research (GIAR) of up to $1,000 (projects in some specific areas may request up to $5,000). If you have any questions about applying for GIAR, contact the Brown University Chapter of Sigma Xi at firstname.lastname@example.org.
Even though this site is aimed more at graduate-level project funding, you might still be able to find funding sources for your project.