...

The preferred and supported method of web services in openmrs is through the REST Module. See that page for how to install and configure the module. You can also read about the REST Web Services API For Clients, and the provided REST Web Service Resources in OpenMRS 1.8.

(There is also an older Unsupported REST Module that provides simple access to patients, obs, and users.  However, this will no longer be supported in favor of the previously mentioned module)

SOAP Web Services

There are several modules that provide SOAP Web Services methods. This only works for OpenMRS 1.6.0+ and is not supported by the core team like the REST Module.