What Bobert said.
There should also be a translucent or white nylon gasket, a big washer, between the sink and the nut. If that is missing, it may be that your nut won't tighten up enough. Plumbers putty is like plasticine. Put enough on that it 'squirts' out as you tighten the nut.
The plastic U-bend trap segments rely on gaskets and cleanliness to be watertight. It is full of dirty water, so keep them straight and take it off in one piece, and spread a towel when you take it off. There will be some spillage.

And when you take it off, DON"T hand it to someone to pour away without specifying where! I did, just once.
Straight into the sink I was working on, it went!

A big channellock pliers should be available at a cheapo toolshop. There isn't really a substitute cheaper, but they last forever.