Fixing a kitchen sink pipe that is leaking
It appears to be leaking at the compression fitting from brass or copper to ABS. Simply tightening the nut there should do, but you may need to disassemble and clean off any calcium deposits to get a good seal. A ChannelLock type plier works well. 

The reason it's leaking, though, is probably because the trap is clogged. You wouldn't normally have enough back-pressure to push water out at that point. If the trap is constructed with similar compression fittings, simply take it a part and clean things out. The clog is probably grease and soap goo.