I read the instructions for this task, purchased the products, and went for it. This would be one of the easier tasks I attempted.
Supplies Pictured:
Cable Lubricant
Plastic bag
Brake Cleaner
Orange Hand Cleaner
Simple Green Cleaner
Paper Towels
Old Newspaper (oooh, $1.99 milk…)
Utility Light
Supplies Not pictured:
Low profile floor jack
Jack Stands
2X4 Wood
Zip ties
Wire cutter
Armor All
Ok, I jacked up the car using the proper procedures, and turned the wheels to the right:
And access the cable behind the driver’s side front wheel. I unscrewed the knurled coupler, but the cable was also zip tied to the brake line. I used a wire cutter to free the cable:
I followed the cable into the rubber grommet, into the body, and unscrewed it from the lamda counter:
The cable was free, so I took it into my work area (kitchen). I removed the cable from its sheathing, and wiped it clean with paper towels. 
I sprayed brake cleaner down the sheathing, and it spurted into my eye. So I read the label on the can, and flushed my eye with water for 10 minutes.
Next I reinserted the cable, and moved it around to free any gunk. I was supposed to drain it into my plastic bag for collection, but I ended up draining it into my sink. Oh well.
I removed the cable once more, dried it off, and reinserted it, this time using several drops of cable lubricant. I cleaned off the sheathing with simple green, and used some Armor All on it.
Then I simply reconnected it. I also used some new wire ties to keep it close to the brake line. I drove the car tonight, and the speedometer needle seems to be steadier at a constant speed, but still vibrates while accelerating. Oh well, at least I’m lengthening its life.
Costs:
Cable Lubricant on eBay: $5.49
Brake Cleaner from Advance Auto Parts: $3.44