In general Memento's Web API's implement the four main HTTP methods (GET, PUT, POST, and DELETE) which can be mapped to CRUD operations as follows:

Memento Work Log API

Action HTTP Method Relative URI
Get a list of all work logs GET /api/worklogs
Get a work log by id GET /api/worklogs/id
Create a new work log POST /api/worklogs
Update a work log PUT /api/worklogs/id
Update a work log PATCH /api/worklogs/id
Delete a work log DELETE /api/worklogs/id

Memento Work Log Reports API

Action HTTP Method Relative URI
Get a work log report for a given user between dates GET /api/worklogreport/?from=1900-07-30-00:00&to=2050-08-02-00:00&personId=1&projectId=1
Get a work log report grouped by project between dates GET /api/worklogreport?group=project&from=2012-07-30-00:00&to=2012-08-02-00:00
Get a work log report grouped by category between dates GET /api/worklogreport?group=category&from=2012-07-30-00:00&to=2012-08-02-00:00