The faucet is secured by a nut from underneath, and it's hard to reach because of the sink basin. You need a special tool called a basin wrench to get up to the nut and tighten it. This picture shows one in use:
The faucet you have has only one threaded piece and nut, but it's the same principle.You can find basin wrenches at the big-box home improvement places and most hardware stores, or you may be able to borrow one from someone who does plumbing repairs. They aren't expensive if you decide to buy one.
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