To have multiple instances accessing one oracle database in your machine, you will need Real Application Clusters (RAC) i.e. the Oracle clusterware 10g services installed. You'll probably need to specify lots of things including what constitutes your voting disks, public network and private network for your cluster interconnect and not to mention the oracle cluster registry (OCR) disks as well.
Of course, all this is intended to allow the separate instances to run on two or more separate server machines with the datafiles out on shared storage - it doesn't make any sense to run multiple instances on one machine, unless they're for different databases. Even then, an instance is a heavyweight entity, lots of overhead even before the first session connects, and it's not overhead you want to take on unnecessarily. Unless applications are poorly designed (and admittedly many are), they're usually able to run in separate sets of schemas within the same database, so it might be worth considering that option.
You could use the Database Configuration Assistant (DBCA) to create new databases on the same server.
Why do you want to do that ? what is the purpose ?
The answer provided fails to point out that RAC is for multiple server machines, each running an Oracle instance working as part of a cluster database, all accessing a common set of datafiles on external shared storage. That’s a fairly complex and expensive thing to configure for real world use (as opposed to a test lab, where you can use cheap hardware and iSCSI over gigabit Ethernet if you’re just trying to learn the technology). I can’t think of a reason in the world to run multiple instances against a single database on a single server – I’m not even sure that the installation software would understand it, as it’s going to be looking for all the things mentioned above (private network, virtual IPs, OCR, etc.), many of which only make sense when configuring 2 or more servers in a cluster.
On reflection, I thought it best to improve the answer to clarify the multi-server intent of RAC, so my earlier comment on the point is no longer relevant.