Some examples in various environments that will help get you started.

cURL

curl --get -H 'Accept: application/json' \
-u username:password \
https://rest.reserve-online.net/availability?location=Athens\&checkin=2017-04-20\&nights=1\&sort_by=POPULARITY

PHP

$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, "https://rest.reserve-online.net/availability?location=Athens&checkin=2017-04-20");
curl_setopt($ch, CURLOPT_USERPWD, "username:password");
curl_setopt($ch, CURLOPT_HTTPAUTH, CURLAUTH_BASIC);
curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, false);
curl_setopt($ch, CURLOPT_CONNECTTIMEOUT, 10);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
$result = curl_exec($ch);
curl_close($ch);

Java

import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.net.HttpURLConnection;
import java.net.URL;

try {
    URL url = new URL("https://rest.reserve-online.net/availability?location=Athens&checkin=2017-04-20");
    String encoding = new sun.misc.BASE64Encoder().encode("username:password".getBytes());

    HttpURLConnection connection = (HttpURLConnection)url.openConnection();

    connection.setRequestMethod("GET");
    connection.setDoOutput(true);
    connection.setRequestProperty("Authorization", "Basic " + encoding);
    InputStream content = connection.getInputStream();
    BufferedReader in = new BufferedReader(new InputStreamReader(content));
    String line;
    while ( (line = in.readLine()) != null ) {
        System.out.println(line);
    }
} catch (Exception e) {
    e.printStackTrace();
}

CFML

<cfhttp
	url="https://rest.reserve-online.net/availability"
	charset="utf-8"
	method="GET"
	result="response"
	timeout="10"
	throwOnError="no">

	<cfhttpparam type="header" name="Authorization" value="Basic #ToBase64('username:password')#">
	<cfhttpparam type="header" name="Accept" value="application/json">
	<cfhttpparam type="header" name="Accept-Language" value="en">
	<cfhttpparam type="URL" name="location" value="Athens">
	<cfhttpparam type="URL" name="checkin" value="2017-04-20">
</cfhttp>