How to create REST URLs without verbs?

General principles for good URI design:

• Don’t use query parameters to alter state
• Don’t use mixed-case paths if you can help it; lowercase is best
• Don’t use implementation-specific extensions in your URIs (.php, .py, .pl, etc.)
• Don’t fall into RPC with your URIs
• Do limit your URI space as much as possible
• Do keep path segments short
• Do prefer either /resource or /resource/; create 301 redirects from the one you don’t use
• Do use query parameters for sub-selection of a resource; i.e. pagination, search queries
• Do move stuff out of the URI that should be in an HTTP header or a body

(Note: I did not say “RESTful URI design”; URIs are essentially opaque in REST.)

General principles for HTTP method choice:

• Don’t ever use GET to alter state; this is a great way to have the Googlebot ruin your day
• Don’t use PUT unless you are updating an entire resource
• Don’t use PUT unless you can also legitimately do a GET on the same URI
• Don’t use POST to retrieve information that is long-lived or that might be reasonable to cache
• Don’t perform an operation that is not idempotent with PUT
• Do use GET for as much as possible
• Do use POST in preference to PUT when in doubt
• Do use POST whenever you have to do something that feels RPC-like
• Do use PUT for classes of resources that are larger or hierarchical
• Do use DELETE in preference to POST to remove resources
• Do use GET for things like calculations, unless your input is large, in which case use POST

General principles of web service design with HTTP:

• Don’t put metadata in the body of a response that should be in a header
• Don’t put metadata in a separate resource unless including it would create significant overhead
• Do use the appropriate status code
• 201 Created after creating a resource; resource must exist at the time the response is sent
• 202 Accepted after performing an operation successfully or creating a resource asynchronously
• 400 Bad Request when someone does an operation on data that’s clearly bogus; for your application this could be a validation error; generally reserve 500 for uncaught exceptions
• 401 Unauthorized when someone accesses your API either without supplying a necessary Authorization header or when the credentials within the Authorization are invalid; don’t use this response code if you aren’t expecting credentials via an Authorization header.
• 403 Forbidden when someone accesses your API in a way that might be malicious or if they aren’t authorized
• 405 Method Not Allowed when someone uses POST when they should have used PUT, etc
• 413 Request Entity Too Large when someone attempts to send you an unacceptably large file
• 418 I'm a teapot when attempting to brew coffee with a teapot
• Do use caching headers whenever you can
• ETag headers are good when you can easily reduce a resource to a hash value
• Last-Modified should indicate to you that keeping around a timestamp of when resources are updated is a good idea
• Cache-Control and Expires should be given sensible values
• Do everything you can to honor caching headers in a request (If-None-Modified, If-Modified-Since)
• Do use redirects when they make sense, but these should be rare for a web service

With regard to your specific question, POST should be used for #4 and #5. These operations fall under the “RPC-like” guideline above. For #5, remember that POST does not necessarily have to use Content-Type: application/x-www-form-urlencoded. This could just as easily be a JSON or CSV payload.