Replacing the cable is fairly easy. Just make sure to release the tension first (using the shifter put the chain in the smallest gear). That will align the holes in the shifter.
The hard part is getting the cable tension correct. That’s best explained via a video but I’d advise starting by turning the barrel adjusters in and then back out one or two turns.
If the housing is old replacing the cable may not help any shifting issues. If you slide off the end caps from the housing and see a couple mm of the individual wires, the housing should be replaced.