The 'best' strategy depends on your requirements; there is no 'one size fits all'. For best efficiency and performance TimesTen should be deployed on the same machine as the application(s) that will be using it and the applications should connect via direct mode rather than client server. But, it all depends on your requirements and objectives. If you can give more details then we can give a better answer.
Our application is running or oracle database.generally on production environment , we are installing oracle on one server and application on another. so i need an expert advice that if we are integrate our application on Timesten then what would be the best way to deploy.
It depends on your current architecture, whether you can accommodate any changes to that architecture, your performance targets and your availability targets.
As I said, in general you should install TimesTen in the application tier, i.e. on the same machine(s) as the applications, and have the applications connect in direct mode. But whether this is feasible depends on how you will be using Timesten, how the applications use the data that is in TimesTen, what kind of HA requirements you have etc. Without that information it is a bit like saying: 'I need to wrote a program, what is the best way to do it'. It is an impossible question to answer without a lot more detail.
Yes, that is normal. Oracle DB lives on its own server in the database tier. TimesTen and the application live together on a different server in the application tier. All the performance critical communication is between the application and Timesten. Communication between TimesTen and Oracle DB is outside the query/transaction path and so is less critical. We do not recommend installing TimesTen on the same server as Oracle DB as that is usually a sub-optimal configuration.
No, there is nothing to install on the Oracle machine. I suggest before you get started you take some time to read the TimesTen documentation and the Installation Guide and Cache User's Guide in particular. And then follow the QuickStart tutorials that lead you through configuring cacheing etc.