How to receive information from users unable to access Appian?

This can be achieved by two ways -
1) Sending emails to trigger a process model - Here is an earlier post - forum.appian.com/.../
2) Publishing a process model as a webservice. The data required to be sent to Appian via this webservice.
Actually there is another way too
Using Custom Servlets
forum.appian.com/.../
For publishing process model as a webservice here is the reference - forum.appian.com/.../Publishing_Process_Models_as_Web_Services

Thankyou for the information

By receiving information from users who are not part of Appian, you lose lot of valuable SLA and KPI based information. It is worth identifying if any of these requirements affect your design. I'd recommend keeping the solution totally out of the box and avoid custom code etc.,
In order to invoke a process as web service, you need to provide a valid user credential as part of the service call.
The other option is to write the data to a database and use query rule (or other means) to poll the data. within the process. But I'd advice caution against 'polling' database as this may not be an efficient design.