Can you clarify the use case. Are you trying to consume a 3rd party SOAP/REST API in C4C or are you trying to consume a C4C SOAP/oData API with a 3rd party app?
In the former, you will need to setup an inbound communication arrangement or data mashup in C4C to consume a 3rd party SOAP/REST API. There will need to be follow-up work to then show the data provided by the 3rd party SOAP/REST API. In the case of SOAP you will need to use SDK to create a custom UI and write some code to call API and render it in the custom UI. In the case of REST, you can use either SDK or KUT HTML-Code mashup to create a simple "front end" UI via HTML.
In the later, you will need to setup an outbound communication arrangement so a 3rd party app can consume a C4C public SOAP/oData API.
We will be releasing a blog series shortly that step through these use-cases in more detail on how you do this with sample scenarios/code.
Thanks,
Rei