To do this you will want to start with a fresh droplet running the 64bit version and install any needed software using apt-get. The steps required will depend on the software you are running or plan to run on the new droplet. You tagged this with nginx so I'll provide some basic information on migrating those services.

I will cover migrating a static site. If you're running a full LEMP stack for PHP applications, follow this guide to set up your environment.

First install nginx:

apt-get update
apt-get install nginx

Now you can copy over your web files from your old server to the new one. Copy the entire directory to the same location on the new server.

Next you can copy your nginx configuration. Copy the files from /etc/nginx/sites-enabled on the old server to the new.

Now restart nginx

service nginx restart

If you have other services running, let me know and I can provide more information.