I am considering writing a new set of applications using OSGi, but they will need to interact heavily with existing non-OSGi applications.
To clarify, the new applications will need to call into existing non-OSGi code bases maintained by other teams (usually propriety services of varying protocols), and new non-OSGi applications will need to call the new OSGi services.
I am not seeing much documentation for how to do this.
Can someone please point me to the correct steps
It sounds like you want to embed OSGi into a larger application. A good starting point for this is a blog post I wrote some time ago: http://njbartlett.name/2011/07/03/embedding-osgi.html
The trick to creating visibility between OSGi bundles and the objects "outside" OSGi is to publish and/or consume services using the system bundle's BundleContext. The embedding code must be aware of the objects from the outer application that you want to make visible into OSGi, and it should publish them as services. Be aware that you need to export the service interface packages via the system bundle exports -- how to do this is described in the blog post.
OSGi services are only for communications inside the same JVM process. So I guess you want to communicate between processes. In this case you have all the usual remoting protocols like SOAP, Rest, RMI. On the OSGi side you can bridge from OSGi services to offering SOAP or REST endpoints using Distributed OSGi (DOSGi).