Unless there are special APIs for this site, you can always study and then send/process the data the way your browser does it.
For instance, an attempt to connect to this site with user='MyName' and password='MyPassword' with Firefox.
Firefox is posting these data:
http://e-services.minagric.gr/UIDL?windowName=1
POST /UIDL?windowName=1 HTTP/1.1
Host: e-services.minagric.gr
User-Agent: Mozilla/5.0 (Windows NT 5.1; rv:32.0) Gecko/20100101 Firefox/32.0
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-Language: fr,fr-fr;q=0.8,en-us;q=0.5,en;q=0.3
Accept-Encoding: gzip, deflate
Content-Type: text/plain;charset=utf-8
Referer: http://e-services.minagric.gr/
Content-Length: 187
Cookie: JSESSIONID=f5bd3f21c4052fc480fd603e9d2a; __utma=214103555.280544018.1411154359.1411154359.1411154359.1; __utmb=214103555.1.10.1411154359; __utmc=214103555; __utmz=214103555.1411154359.1.1.utmcsr=forum.lazarus.freepascal.org|utmccn=(referral)|utmcmd=referral|utmcct=/index.php/topic,25874.msg157916/topicseen.html
Connection: keep-alive
Pragma: no-cache
Cache-Control: no-cache
b1cd3dcf-7e5b-4aad-aa6f-02c135acb2cf[1D]MyName[1F]PID29[1F]text[1F]s[1E]6[1F]PID29[1F]c[1F]i[1E]MyPassword[1F]PID30[1F]text[1F]s[1E]10[1F]PID30[1F]c[1F]i[1E]true[1F]PID31[1F]state[1F]b[1E]1,245,435,false,false,false,false,1,34,16[1F]PID31[1F]mousedetails[1F]s
HTTP/1.1 200 OK
Server: GlassFish Server Open Source Edition 3.0.1
Content-Type: application/json;charset=UTF-8
Transfer-Encoding: chunked
Content-Encoding: gzip
Vary: Accept-Encoding
Date: Fri, 19 Sep 2014 19:25:20 GMT
----------------------------------------------------------
The interesting part is the post data themselves, of course:
b1cd3dcf-7e5b-4aad-aa6f-02c135acb2cf[1D]MyName[1F]PID29[1F]text[1F]s[1E]6[1F]PID29[1F]c[1F]i[1E]
MyPassword[1F]PID30[1F]text[1F]s[1E]10[1F]PID30[1F]c[1F]i[1E]true[1F]PID31[1F]
state[1F]b[1E]1,245,435,false,false,false,false,1,34,16[1F]PID31[1F]mousedetails[1F]s
You'll probably have to also study the html/javascript source code of the connexion page, in order to understand which and how the data are processed.
Another possible solution is to try an embedded browser solution (sorry, this one is not in my domain, and I can't give any advices for this solution).