How do you connect 4 stranded copper wires together?

With a properly sized wire nut. IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB

SAFELY AND COMPETENTLY

REFER THIS WORK TO QUALIFIED PROFESSIONALS. If you do this work yourself, always turn off the power at the breaker box/fuse panel BEFORE you attempt to do any work AND always use an electrician's test meter having metal-tipped probes (not a simple proximity voltage indicator) to insure the circuit is, in fact, de-energized.