Typically there is one COPYING file at the root of the project. You can find some guidelines on how the Free Software Foundation suggests to apply the GNU Licenses (e.g. GPL, LGPL) to your software:
For the Apache Software License - which you have not asked for but just to give a second example - does this a little different due to differences in the license. For it, typically there is one LICENSE and if applicable a NOTICE file at the root of the project. You can find some guidelines on how the Apache Foundation does it here: