Well it kindakind of depends on what resources you already have. For instance if the application uses all the cores on the computer, simply spinning up another instance of the application won't necessarily mean that requests get handled faster because the two applications would be sharing the resources on the server.
The important thing to remember here is that generally it doesn't make much sense to spin up another instance of the application which would end up using the same resources as the first instance (for example if they try to access the same hard drive at the same time, the operating system has to keep switching access to the hard drive between the two applications).
Most multi-server environments use load balancers to automatically distribute requests between physical machines (see the link in JeffO's answer or https://azure.microsoft.com/en-gb/documentation/articles/load-balancer-overview/) so one of the things you have to keep in mind when programming for scalability, is that one client might not always have every request handled by the same server.