how to create an issue in jira via rest api?

As of the latest released version (4.3.3) it is not possible to do using the REST API. You can create issues remotely using the JIRA SOAP API.

See this page for an example Java client.

The REST API in JIRA 5.0 contains methods for creating tasks and subtasks.

(At time of writing, 5.0 is not yet released, although you can access 5.0-m4 from the EAP page. The doco for create-issue in 5.0-m4 is here).

POST to this URL

https://<JIRA_HOST>/rest/api/2/issue/

This data:

{
"fields": {
   "project":
   { 
      "key": "<PROJECT_KEY>"
   },
   "summary": "REST EXAMPLE",
   "description": "Creating an issue via REST API",
   "issuetype": {
      "name": "Bug"
   }
  }
}

In received answer will be ID and key of your ISSUE:

{"id":"83336","key":"PROJECT_KEY-4","self":"https://<JIRA_HOST>/rest/api/2/issue/83336"}

Don't forget about authorization. I used HTTP-Basic one.