First make sure the line’s ends match, since a connector on the wrong water supply connection may leak. Then check the washer is seated in the nut, take off any thread tape (these seal with washers), and tighten to the package instructions.
Turn the water off at the shutoff valve before you take anything apart. Have a towel and a small bucket under the valve.
Check these in order
The ends don’t match
How to tell: The nut started hard or sits crooked. Compare the sizes on the old line’s package with the valve outlet (usually 3/8" compression) and the fixture end (1/2" FIP for a faucet, 7/8" ballcock for a toilet).
Fix: Fit a line with the right ends. See supply line sizes.
Tape, putty or a missing washer
How to tell: There’s white tape or putty on the threads, or the washer inside a nut is missing, doubled or twisted.
Fix: Clean the threads and seat the washer flat. The connector comes with washers, so don’t use thread sealant. Putty or gasket material can introduce dirt at the connection.
Too loose, or too tight
How to tell: It drips at the nut (too loose), or the nut or fill valve is cracked (too tight).
Fix: Follow the instructions for that line. On a BrassCraft line, the faucet end is hand-tight only; at a 3/8" compression valve, go hand-tight then a wrench 1/4 turn more. Tighten a Fluidmaster toilet fill valve nut by hand, and if it leaks at the tank, turn it “just enough to stop leaking”; overtightening can damage the fill valve.
The line is old
How to tell: Kinked, rusty, frayed or more than 5 years old.
Fix: Replace it with a new connector.
Leaking where the pipe goes into the valve
That’s the valve’s own compression joint (a nut and brass sleeve on the pipe), not the supply line. The pipe must be cut square, round and free of burrs, and the valve must sit square on the pipe. Tighten 3/4 turn past hand-tight, but don’t overtighten, which can crack it. No tape, putty or gasket material on a compression joint either. If it still leaks, replace the valve: see shutoff valves for copper and for PEX.