All the examples on the web of socket usage are as complicated as possible, because that is helpful. Thanks morons. Anyway, here's a simple example.

simple_socket_client.c

#if _WIN32
#include <winsock2.h>
#else
#include <arpa/inet.h>
#include <netinet/in.h>
#include <sys/socket.h>
#endif

#if __APPLE__ || _WIN32
#define MSG_NOSIGNAL 0
#endif
#if _WIN32
#define close(x) closesocket(x)
#endif

void simple_socket_example(sp_session *session) {
    struct sockaddr_in serv_addr = {
        .sin_family = AF_INET,
        .sin_port = htons(13581),
        .sin_addr = { .s_addr = INADDR_ANY }
    };
    int sockfd = socket(AF_INET, SOCK_STREAM, 0);
    connect(sockfd, (struct sockaddr *)&serv_addr, sizeof(serv_addr));
    send(sockfd, "hello there!\n", 13, MSG_NOSIGNAL);
    close(sockfd);
}