ENDPOINT :  /rest/V1/guest-carts/{cartId}/shipping-information

e.g : http://localhost.magento.com/rest/V1/guest-carts/DnsT4UjkMPPdID4K53h4ToaXMSElc8pI/shipping-information

METHOD : POST

HEADERS : Content-Type application/json

                    Authorization : Bearer

PAYLOAD:
  
{  "addressInformation": {
       "shipping_address": {
       "region": "New York",
       "region_id": 43,
       "region_code": "NY",
       "country_id": "US",
       "street": [
      "123 Oak Ave"
    ],
    "postcode": "35004",
    "city": "Purchase",
    "firstname": "Jane",
    "lastname": "Doe",
    "email": "jdoe@example.com",
    "telephone": "512-555-1111"
  },
  "billing_address": {
    "region": "New York",
    "region_id": 43,
    "region_code": "NY",
    "country_id": "US",
    "street": [
      "123 Oak Ave"
    ],
    "postcode": "35004",
    "city": "Purchase",
    "firstname": "Jane",
    "lastname": "Doe",
    "email": "jdoe@example.com",
    "telephone": "512-555-1111"
  },
  "shipping_carrier_code": "freeshipping",
  "shipping_method_code": "freeshipping"
  }
}
                                   // We are passing shipping and billing address with shipping code.                                                        You  can change the address as well as shipping method of your choice

Response :
 
 {
    "payment_methods": [
        {
            "code": "cashondelivery",
            "title": "Cash On Delivery"
        },
        {
            "code": "banktransfer",
            "title": "Bank Transfer Payment"
        },
        {
            "code": "checkmo",
            "title": "Check / Money order"
        }
    ],
    "totals": {
        "grand_total": 27,
        "base_grand_total": 27,
        "subtotal": 32,
        "base_subtotal": 32,
        "discount_amount": -5,
        "base_discount_amount": -5,
        "subtotal_with_discount": 27,
        "base_subtotal_with_discount": 27,
        "shipping_amount": 0,
        "base_shipping_amount": 0,
        "shipping_discount_amount": 0,
        "base_shipping_discount_amount": 0,
        "tax_amount": 0,
        "base_tax_amount": 0,
        "weee_tax_applied_amount": null,
        "shipping_tax_amount": 0,
        "base_shipping_tax_amount": 0,
        "subtotal_incl_tax": 32,
        "shipping_incl_tax": 0,
        "base_shipping_incl_tax": 0,
        "base_currency_code": "USD",
        "quote_currency_code": "USD",
        "items_qty": 1,
        "items": [
            {
                "item_id": 26,
                "price": 32,
                "base_price": 32,
                "qty": 1,
                "row_total": 32,
                "base_row_total": 32,
                "row_total_with_discount": 0,
                "tax_amount": 0,
                "base_tax_amount": 0,
                "tax_percent": 0,
                "discount_amount": 0,
                "base_discount_amount": 0,
                "discount_percent": 0,
                "price_incl_tax": 32,
                "base_price_incl_tax": 32,
                "row_total_incl_tax": 32,
                "base_row_total_incl_tax": 32,
                "options": "[]",
                "weee_tax_applied_amount": null,
                "weee_tax_applied": null,
                "name": "Strive Shoulder Pack"
            }
        ],
        "total_segments": [
            {
                "code": "subtotal",
                "title": "Subtotal",
                "value": 32
            },
            {
                "code": "discount",
                "title": "Discount (You Save)",
                "value": -5
            },
            {
                "code": "shipping",
                "title": "Shipping & Handling (Free Shipping - Free)",
                "value": 0
            },
            {
                "code": "tax",
                "title": "Tax",
                "value": 0,
                "extension_attributes": {
                    "tax_grandtotal_details": []
                }
            },
            {
                "code": "testdiscount",
                "title": "Discount (You Save)",
                "value": -5
            },
            {
                "code": "grand_total",
                "title": "Grand Total",
                "value": 27,
                "area": "footer"
            }
        ]
    }
}                              // return all the available payment methods with cart information