I have been able to create my ftp server with vsftpd and I can get access to it locally, I mean without internet...but I want to have access to it over tcp or internet...help?
You can use some software for example filezilla for connecting to your ftp server. download it from there: filezilla
This is really a complex question. Yes, you are correct, it is easy to do when you are on same network inside house, work, etc...
The vague answer is that if you have a router, you will have to get logged into it, open a port to be able to get connected, but that may still be a problem because of ISP provider changing IP Addresses on you randomly. You will probably have to use a online dns service as well as possibly a few other tricks.
Depending on what your needs are a cloud drive service is much easier solution.
Just read your comment about the samsung phone.
This app says it makes it possible to forward ports on a phone tethering connection. It may be what you need. I have no direct experience using it:
-- Original answer:
To help you out, we need more information. Please provide us with answers to the following:
Output of ifconfig on the ftp server:
Do you have access to the configuration of your network router?
Is this going to be a publicly accessable FTP, or do you want to limit access and is security a concern?