The simplest method is to simply use commonly available tools.
The basic "dig" command will return the records to you via this query:
dig mx example.com
If you want just the lines with the mx records...
dig mx example.com | grep -v '^;' | grep example.com
dig is available on most linux / unix boxes.
If you're on windows you can use nslookup
nslookup -type=mx example.com
Then just parse the output of these common tools.
EDIT: Simple C example of sockets from the web
Since you put "C" as a tag, I guess you're looking for source code to do MX lookups using raw sockets. I copied this from http://www.developerweb.net/forum/showthread.php?t=3550. It may be more what you're looking for?
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <netinet/in.h>
#include <resolv.h>
int main (int argc, char *argv[])
{
u_char nsbuf[4096];
char dispbuf[4096];
ns_msg msg;
ns_rr rr;
int i, j, l;
if (argc < 2) {
printf ("Usage: %s <domain>[...]\n", argv[0]);
exit (1);
}
for (i = 1; i < argc; i++) {
l = res_query (argv[i], ns_c_any, ns_t_mx, nsbuf, sizeof (nsbuf));
if (l < 0) {
perror (argv[i]);
} else {
#ifdef USE_PQUERY
/* this will give lots of detailed info on the request and reply */
res_pquery (&_res, nsbuf, l, stdout);
#else
/* just grab the MX answer info */
ns_initparse (nsbuf, l, &msg);
printf ("%s :\n", argv[i]);
l = ns_msg_count (msg, ns_s_an);
for (j = 0; j < l; j++) {
ns_parserr (&msg, ns_s_an, j, &rr);
ns_sprintrr (&msg, &rr, NULL, NULL, dispbuf, sizeof (dispbuf));
printf ("%s\n", dispbuf);
}
#endif
}
}
exit (0);
}