Download from Oracle:
Express Edition release for Windows
OracleXE.exe 165 MB
or grab a copy here in the lab from \\kadenix\public\OracleEX.exe
Install: take all the defaults. If some problem, Oracle 10g XE Documentation Home page read the Installation Guide.
I installed on a desktop and a laptop without incident (except laptop
needed more RAM [it won't install if less than 256MB; Oracle takes a
lot of RAM, system will be sluggish if only has 256MB]).
It will install as an automatic service (i.e. will automatically start at boot). If you don't want that, use the Services administrative tool to change OracleServiceXE to Manual and start and stop it via the All Programs menu (or the desktop icons).
For running on Linux: Oracle 10g XE on Linux notes