1-) Set Log Directory path in Tools->Preferences->Environment
2-) At sqldeveloper\sqldeveloper\bin directory edit sqldeveloper.conf file, comment out "IncludeConfFile sqldeveloper-nondebug.conf" and "IncludeConfFile sqldeveloper-debug.conf"
#IncludeConfFile sqldeveloper-nondebug.conf
IncludeConfFile sqldeveloper-debug.conf
Restart sql developer. You will see that debug logs will be created under log directory with the name format SQLDeveloper_YYYYMMDDHH24MISS.log
In order to add kerberos debugging you shoud add following java option to sqldeveloper.conf file at sqldeveloper\sqldeveloper\bin directory
AddVMOption -Dsun.security.krb5.debug=true
However kerberos debug information will not be written to sql developer debug log file. It is send to stdout. In order to get kerberos debug output you should start sql developer from command line. Set screen buffer size of cmd window to some value higher then the system default so some debug output will not be lost because of small buffer size.