A kitchen faucet replacement is a small job that goes wrong in a few specific places. The trouble almost always comes from the shutoff valves, the supply lines, or a fitting that was not tightened in the right order. If you move through the work in the sequence below, you will find those places before water does.
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Before you go under the sink
Clear everything out from under the cabinet and put a towel and a shallow bucket down. Find the two shutoff valves, one for hot and one for cold, on the supply lines. Turn each one clockwise until it stops. If a valve will not turn, or turns and then drips, do not force it. Stop there and call a plumber to look at the valves, because a broken shutoff is a different job. Then turn on the faucet and let the water run until it stops, which tells you the valves are holding.
Take a photo of the connections before you touch them. Note which line goes to hot and which to cold, and how the existing supply lines are attached. Buy the replacement with supply lines long enough to reach without strain, and check that the mounting hardware matches the holes in your sink.
Remove the old faucet
Disconnect the supply lines from the valves first, with a bucket underneath to catch the water left in the lines. Then loosen the mounting nuts under the sink. These are often stuck, so use steady pressure instead of jerking. Lift the old faucet out from above, and clean the surface of the sink where the base sat. Old sealant or gasket material should be scraped away so the new one seats flat.
Set the new one
Place the new faucet through the holes, following the instructions that came with it, and tighten the mounting hardware from underneath by hand first. Then snug it with a wrench, a little at a time, so the base does not rock or crack the sink. Connect the supply lines to the valves by hand, and then tighten each connection gently. Overtightening is the most common way a new connection starts to drip.
Connect and test
Open the shutoff valves slowly, one at a time. Turn the faucet on, hot first and then cold, and let the water run for a minute on each side. Check every connection with a dry paper towel. Look at the valves, the nuts under the sink, and the points where the hoses join the faucet. If a towel shows moisture, shut the valve, tighten the connection a small amount, and check again.
Watch it overnight
Leave the towel in place under the sink and check it the next morning. A dry towel after a full day of ordinary use is a good sign that the connections are sound. If you find moisture, do not wait for it to spread. Turn off the valves and call a plumber, and tell them exactly which connection was wet.
What to do tonight
Find the shutoff valves and turn them through a full cycle, stopping if either one is stiff or leaks. Then tell your father what you found. He likely knows the sink better than anyone, and a few minutes of his memory about the old faucet can save you an hour of guessing.