I created RemoteFieldValues for the items I wanted to update. The first field is the property you want to change, and the second is a String array containing the value you want to change it to. The value is usually a String id associated with that type. For example, the resolution "Fixed" has the id 1 so I would pass a String array with value 1. You can call getResolutions(token) to get a list of the available resolutions and to get the id call getId() on one of the resolutions.
String resolution[] = {"1"};
...
RemoteFieldValue resolutionField = new RemoteFieldValue("resolution", resolution);
RemoteFieldValue priorityField = new RemoteFieldValue("priority", priority);
RemoteFieldValue assigneeField = new RemoteFieldValue("assignee", assignee);
Then I created a RemoteFieldValue array with each of the RemoteFieldValues. The order in the array didn't seem to matter.
RemoteFieldValue[] remoteFields = {priorityField, assigneeField, resolutionField};
Before you can call progressWorkflowAction, you have to find the action id. This can be found on your JIRA install if you go to the administration page and go to the Global Settings section. You should find Workflows and you can choose the workflow you are working with. For our installiation, Resolve Issue has an action id of 5. I think you can also find this from a soap call but I can't remember what method it would be. Once you have that and the issueKey you can go ahead and make the call.
progressWorkflowAction(token, issueKey, action, remoteFields);
So that's all I did. You can also update more values such as the summary if you add another value to the RemoteFieldValue array. I'm sure you know where the documentation is but I'll post it anyways
http://docs.atlassian.com/software/jira/docs/api/rpc-jira-plugin/latest/index.html?com/atlassian/jira/rpc/soap/JiraSoapService.html . Also if you run the JIRA Maven2 SOAP Library extension with eclipse, you will get an error telling you if you're missing a field or if something isn't passed correctly. It can be found here
http://confluence.atlassian.com/display/JIRAEXT/JIRA+Maven2+SOAP+Library .