Used Let's Encrypt to secure Ubuntu 14.04/Nginx server (failed tutorial)

Are you sure you followed whole tutorial you linked? As far as I see, there is no any directive for SSL. Also it is listening on HTTP (80) port instead of HTTPS (443). [How To Secure Nginx with Let’s Encrypt on Ubuntu 14.04] describes what you need to change in Nginx config file to use SSL.

First of all make sure you created Diffie-Hellman Group located at /etc/ssl/certs/dhparam.pem. If you did it, make sure you follow said tutorial from Step 3 — Configure TLS/SSL on Web Server (Nginx).

Your server block should look something like:

server {
    listen 443 ssl default_server;
    listen [::]:443 ssl default_server;
    server_name example.com www.example.com; # Replace with your domain

    ssl_certificate /etc/letsencrypt/live/example.com/fullchain.pem;
    ssl_certificate_key /etc/letsencrypt/live/example.com/privkey.pem;

    root /usr/share/nginx/html;
    index index.html index.htm;

    client_max_body_size 10G;

    ssl_protocols TLSv1 TLSv1.1 TLSv1.2;
    ssl_prefer_server_ciphers on;
    ssl_dhparam /etc/ssl/certs/dhparam.pem;
    ssl_ciphers 'ECDHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-AES256-GCM-SHA384:DHE-RSA-AES128-GCM-SHA256:DHE-DSS-AES128-GCM-SHA256:kEDH+AESGCM:ECDHE-RSA-AES128-SHA256:ECDHE-ECDSA-AES128-SHA256:ECDHE-RSA-AES128-SHA:ECDHE-ECDSA-AES128-SHA:ECDHE-RSA-AES256-SHA384:ECDHE-ECDSA-AES256-SHA384:ECDHE-RSA-AES256-SHA:ECDHE-ECDSA-AES256-SHA:DHE-RSA-AES128-SHA256:DHE-RSA-AES128-SHA:DHE-DSS-AES128-SHA256:DHE-RSA-AES256-SHA256:DHE-DSS-AES256-SHA:DHE-RSA-AES256-SHA:AES128-GCM-SHA256:AES256-GCM-SHA384:AES128-SHA256:AES256-SHA256:AES128-SHA:AES256-SHA:AES:CAMELLIA:DES-CBC3-SHA:!aNULL:!eNULL:!EXPORT:!DES:!RC4:!MD5:!PSK:!aECDH:!EDH-DSS-DES-CBC3-SHA:!EDH-RSA-DES-CBC3-SHA:!KRB5-DES-CBC3-SHA';
    ssl_session_timeout 1d;
    ssl_session_cache shared:SSL:50m;
    ssl_stapling on;
    ssl_stapling_verify on;
    add_header Strict-Transport-Security max-age=15768000;

location / {
    proxy_pass http://allthemoore.com:2368;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header Host $http_host;
    proxy_set_header X-Forwarded-Proto $scheme;
    proxy_buffering off;
}
# Redirect all HTTP (80) traffic to HTTPS (443)
server {
    listen 80 default_server;
    listen [::]:80 default_server;
    server_name example.com www.example.com;
    return 301 https://www.$server_name$request_uri;
}

If you created some other config file in /etc/nginx/sites-available make sure you made symbolic link from /etc/nginx/sites-available/example.com to /etc/nginx/sites-enabled. Also make sure old one is disabled.

Make sure you restarted or reloaded nginx sudo systemctl restart nginx. Don’t forget to change example.com to your domain ;)