Which brand? Most likely SRAM. If so, I use 7-speed SRAM MRX shifters and 9-speed SRAM X.9 shifters. Here's what I've found:

MRX: take them apart. I CANNOT get a new cable to thread thru, even one with a soldered tip. Remove them from the bike, and pinch the 4 white plastic retainers inside the black twist-grip - once all four are displaced inward, the twist-grip will slide off over them, and the shifter can be dis-assembled. Observe closely the position of all parts and you'll be able to re-assemble after you've put in a new cable (with patience and a few curses).

X.9: If you've a new cable with a soldered tip, it can be threaded thru pretty easily, following SRAM's instructions. If not, dis-assemble much as above.

Good luck!