Shut off both shut-off valves under the sink. Open the kitchen faucet (both hot and cold) until water stops flowing — this releases the pressure left in the lines and tells you the shut-offs are doing their job. If water keeps trickling after a minute, one of the shut-offs isn't fully closing, and you'll need to address that before you go any further. (More on that in a moment.)
With the lines depressurized, slide the bucket under the supply-line connections at the shut-off valves. Disconnect the cold-side line first — the supply nut at the valve is usually accessible with an adjustable wrench. Then move to the supply nuts at the top of the faucet body, where the basin wrench earns its keep. The basin wrench's hinged jaw lets you grip a nut you can barely see, much less reach with a normal wrench. Apply firm, steady pressure in the direction the wrench wants to turn — counterclockwise when looking up. If the nut doesn't break free in five or six seconds, stop. Don't crank harder.
This is where the project most commonly stretches past two hours, and the move is to be patient instead of forceful. Spray a generous shot of penetrating oil at the joint between the supply nut and the faucet shank. Walk away for ten minutes. Make a coffee. Come back, give the nut a gentle tap with a screwdriver handle to break any mineral seal, and try again. Eight times out of ten, the nut releases on the second attempt. It's the kind of small patience that distinguishes a homeowner who finishes the job from one who sends a frustrated text to the family group chat at 11:30 a.m.
Once both supply lines are off, find the mounting hardware below the faucet — typically a horseshoe-shaped bracket and a single threaded mounting nut on most modern faucets, or a pair of threaded studs with wing nuts on older designs. Loosen and remove. Lift the old faucet up through the deck. Wipe the deck clean of old plumber's putty, silicone residue, or mineral scale; a plastic scraper and a damp cloth do the work without scratching the sink.