How do I send data to Appian, to start a process model from third party applicat

you can use a servlet plugin to do so. In that case data from third party application will be sent through that plugin to your process model. In your process model you should declare variables as parameter (who are required to start your process).

can you direct me to the servlet plugin?
I want to pass in the data from third party application to embedded interface which would start a process.

you can go through developer documentation on forum to understand servlet plugin.

as per my understanding, we have to create a servlet plugin, they are not already made to carry out functions.

yes right.

is there anything which already exists?

forum.appian.com/.../Publishing_Process_Models_as_Web_Services.html

Would be be your best way

You could use a web API in conjunction with the start process writer plugin, or simply have appian receive an email and start the process.

you can have a look in shared components section, but i doubt about it. If you get something existing , you still have to make changes in it according to your requirements.

...or the above!