I haven't worked on that particular shifter, but on most Shimano shifters of the type there is a little cap opposite where the cable enters with a Philips head fitting. Shift into the highest gear (lowest cable tension), disconnect the cable, remove the cap by unscrewing it (it only takes a turn or two), and then push the cable into the shifter. The cable head should exit through the hole vacated by the cap. A new cable can be inserted through the hole and the process reversed to hook it up.
Manual describing the process here: