There are several options for this. One quite easy way is that you create a database link between the databases. See:
http://download.oracle.com/docs/cd/B14117_01/server.101/b10759/statements_5005.htm[
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Using that link you can execute statements against the remote server for example from a trigger in the source server.
If you're looking for a solution where the remote server acts as a backup server, then have a look at standby solutions:
http://download.oracle.com/docs/cd/B19306_01/server.102/b14239/create_ps.htm[
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[Addition based on comment]
You can create two separate connection objects and execute necessary statements against both connections.
However, if you plan to do the exact same things on both server I believe that this will only succeed generally if there's 1 and only 1 user in both databases at the same time. If they are multi-user databases another application may interfere the logic in the middle of an operation and the results may vary among those databases.
Another thing is that what's going to happen if you execute DML operation against database 1 and then against database 2. What if the second operation isn't succeeding? By definition you should roll back the first operation also but can you do this reliably from the client application. Typically a distributed transaction is used in these kind of cases.
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