How do I fix a couch with a protruding spring?
One of your spring wires is slipping sideways and poking your upholstery. The spring wires are held to the sinuous springs by metal clips; apparently that wire's clips are loose and are allowing the spring wire to get out of place. (Has someone been jumping on your couch?)

Your first step is to get access to the underside of the couch. Yes, you have to take off the dust cover fabric that covers the bottom of your couch and keeps your cats from hiding there, but there's nothing to be done.

With the dust cover off, you can try to slide the spring wire back into place. My guess is that's going to be very difficult, as those clips are pretty strong (although apparently not strong enough), but if it works then good on you. If not, then you'll have to cut the excess spring wire off, close to the nearest sinuous spring. The wire is quite hard (much harder than copper wire), so you'll need a good pair of cutters to handle it, otherwise you'll damage the cutters.

Now, you need to tighten the metal clips on that wire, and probably on all the wires unless you mind risking another wire going walkabout. Here, you'll need a strong pair of pliers or vice-grips. The goal is to prevent that spring wire from sliding further.

Finally, reattach the dust cover (which doesn't need to look good, unless your guests are in the habit of lifting up and examining the bottom of your couch).