You need to know the custom field ID of the field in question. If the ID is 14, you can use:
<www_path>?entity=activity&action=create&activity_id=0&target_contact_id=0&custom_14=myvalue
In general, if you're asking these sorts of questions, you can answer them best by using the API explorer: Help menu > Developer > API Explorer. You can use it to design your query, and it will build your REST string for you - including looking up custom field IDs.
To get the ID via the GUI, you can go to Administer menu > Customize Data and Screens > Custom Fields, then select "View and Edit Custom Fields" for the appropriate group. If you hover your mouse over the "Edit Field" link, you'll see a URL that ends in "&id=x". "x" is your field ID.
To get the field ID via the API, do a call to CustomField.get. Here's a REST call to get the ID of a field called "Mail Designation":
/sites/all/modules/civicrm/extern/rest.php?entity=CustomField&action=get&json={"sequential":1,"label":"Mail Designation"}&api_key=yourkey&key=sitekey
Better still, use CustomField.getvalue to return just the ID:
/sites/all/modules/civicrm/extern/rest.php?entity=CustomField&action=getvalue&json={"sequential":1,"return":"id","label":"Mail Designation"}&api_key=yourkey&key=sitekey