To create a deal, following permissions are required.

Deal permission: the user should have a permission to manage deals.
Pipeline-specific permission: the user should have a permission to manage the pipeline a new deal belongs to.

By default, primary contact and deal stage are also returned in the response.

{
  "deal": {
    "contact": "51",
    "account": "45",
    "description": "This deal is an important deal",
    "currency": "usd",
    "group": "1",
    "owner": "1",
    "percent": null,
    "stage": "1",
    "status": 0,
    "title": "AC Deal",
    "value": 45600,
    "fields": [
      {
        "customFieldId": 1,
        "fieldValue": "First field value"
      },
      {
        "customFieldId": 2,
        "fieldValue": "2008-01-20"
      },
      {
        "customFieldId": 3,
        "fieldValue": 5500,
        "fieldCurrency": "EUR"
      }
    ]
  }
}