This archive includes both SQL Developer and an embedded copy of the Java 8 Development Kit (JDK). Simply extract the zip to a fresh directory and run the sqldeveloper.exe in the top directory. The EXE is configured to run the embedded JDK by default.

Note: the Windows EXE requires a MSVCR100.dll to run. Most computers will already have this file and in the Windows PATH. However, if the first copy of the file found by the EXE is a 32-bit copy of the DLL, then SQL Developer will fail to start. You can fix this by copying a 64-bit version of the DLL into the BIN directory or updating your OS PATH such that a 64 bit copy of the DLL is found first.