I live in the city so I am on city water. Just recently My cold water only dribbles into my washing machine. Help Please!

Check the cold water supply valve to ensure it is completely open. Look for kinks or any deformity in the hose leading from that fixture to the washing machine.
Turn off the cold water supply then disconnect the cold water hose from the washer. Have a bucket handy! Turn the valve on to see if sufficient pressure is delivered to the washer. If not, the problem is in the plumbing. If water flow is available, the problem is within the washer