A simple HTTP POST request is used to send the input graph and retrieve its the layouted version. You can just perform your own request to the correct URL and pass all required information. However, as we might change internal APIs we recommend you to use the (very small) wrapper implementations we provide for a specific language. We do not provide a wrapper for each language, feel free to write your own and contact us so we can add it to the list below.
You might want to have a look at the Live section of our exemplary server at http://layout.rtsys.informatik.uni-kiel.de:9444 to play around.
Each zip archive contains the wrapper class you can use to call our service as well as a small example illustrating the usage pattern for the specific language.