Summarize this article:

Each county in Oregon has a county elections office. You can find addresses and phone numbers for each office here. Go to your local elections office during its hours of operation. Ask someone on staff to assist you with your voter registration. You will need to provide your driver's license number or the last four digits of your social security number. If you do not have those, you can provide some other photo ID, a paycheck stub, utility bill, bank statement, government document, or proof of eligibility under the Uniformed and Overseas Citizens Absentee Voting Act or the Voting Accessibility for the Elderly and Handicapped Act. The staffer will provide you with any necessary voter registration forms. Allow a few minutes to complete the paperwork.  If you are homeless, provide the address of the place where you sleep, or enter the address of the county clerk. You can always pick up a ballot from the county clerk's office.  If you are concerned about your safety or privacy, request and fill out an Application to Exempt Residence Address from Disclosure as a Public Record (SEL 550).

Summary:
Locate your county elections office. Visit the elections office. Fill out your forms.