An upgrade from Oracle 10.1 to Oracle 10.2 is a big deal, MUCH bigger than just applying a patch. You will have to install the base release 10.2.0.1 into a new Oracle home on your database server, apply the 10.2.0.3 patchset and the latest quarterly critical patch update. Then you can either export/import data from your 10.1.0.4 database into a new 10.2.0.3 database or run some upgrade utilities to convert the old database to run from the 10.2 home.
This is an extremely complicated subject. If you have access to Metalink please read note 316889.1, which gives a 47 step upgrade process from various previous Oracle releases, including 10.1.
As a general rule, anything as complicated as an upgrade to a new release of Oracle needs to be carefully planned and extensively tested in an expendible test environment. You should also develop a well-thought-out backout plan in case the upgrade runs into an unexpected glitch.