Go to Responsibility or Step "Properties" and select "User" as "Assign Type" (1):

Click "Add Users" link (2) to show a popup with users picker (3). Select one or more users (up to 10) by simple mouse clicking (selected users will be highlighted with light blue):

Click "Add" button. Added users will be shown under "Assign Type" field:

Click "Remove User" button (5) to get rid of unneeded assignee.

Select "Field" as "Assign Type" and click "Add Fields" button (6) to call a Fields Picker (7):

Select necessary field(s) (up to 5) by mouse clicking and click "Add" button. The added fields will be shown under "Assign Type":

Select one of these types in "Assign Type" field and click proper "Add..." link to show proper picker (8):

Select a Group / Chatter Group / Queue / Role / Profile / Permission set  (only one can be selected) or Resource / Resource Pool (up to 10) and click "Add" button. The selected assignee(s) will be shown under "Assign Type":

Select "Variable" in "Assign Type" field and click "Add Variable" link to show variables picker (9):

Select a variable (only one allowed) and click "Add" button. Selected variable will be shown under "Assign Type" field:

Select "Call Apex" in "Assign Type" field and click "Add Apex Class" link to show classes picker (11):

Select necessary class and click "Add" button. Selected lass will be shown under "Assign Type":

Example:

Based on Responsibility name code below defines different assignees for each Responsibility:

global with sharing class WR_ApexAssignees implements WR_BPM.WorkflowAssigneeInterface {
     public String execute(sObject context, WR_BPM__Flow_Instance_Cursor__c flowInstanceCursor, WR_BPM__Flow_Step_Junction__c step)
     {
        if(step.WR_BPM__Flow_Swimlane__r.name == 'Responsibility A')
        {
            // code to query assignee data
            // process name is: WR_BPM__Flow__r.WR_BPM__Process__r.Name
            // version (flow) name is: WR_BPM__Flow__r.Name
            return '0056A000000YP12';
        }
        else if (step.WR_BPM__Flow_Swimlane__r.name == 'Responsibility B')
            return '0056A000000YP1M,0056A000000YP12';
        else if(step.WR_BPM__Flow_Swimlane__r.name == 'Responsibility C')
            return '00e6A000000E1aG';
        else if(step.WR_BPM__Flow_Swimlane__r.name == 'Responsibility D')
            return '00G6A000000LjpX';
        else
            return null;
     }
}

Available from version 5.0

Select "Query" as "Assign Type. By default query conditions are not set, so, click "set" link (12) to show "Edit Query Conditions" popup (13):

Set necessary query conditions (14) and click "Apply" button (15). Query information will be shown under "Assign Type":

Click "Edit" link (16) to change Query conditions.

• Resource can be used as is. See proper article.
• Resource Pool needs some configuring, see proper article.

Responsibility or step can be assigned to system for automatic processing.

To make Responsibility system just check "System" checkbox (17):

and confirm this in the popup appeared:

To make particular step system (automatic) select proper option (18) in the "Step Type" picklist:

Also step can be added as automatic initially by dragging proper shape from "Elements" section of left sidebar.