Of course, you can play this game with a partner through Internet, only need is to connect with him. There have two methods to connect with your partner.
If you know your partner's IP address on Internet, you can let your partner check if his "Host" item in "Network" menu (it's also a toolbar button) is checked, and then you can click at "Call" item in "Network" menu (it's also a toolbar button). Input your partner's IP address in the popped up dialog, you will been connected each other and begin your Internet playing.
I suggest you install ICQ, so you can start NetTETRIS from ICQ, and don't need know your partner's IP address. Select "Internet Telephony/Games" in ICQ's user menu, and click at "NetTETRIS", after your partner accept you call, ICQ will start NetTETRIS, you had been connected each other, that's all.
One host only can accept one call, when you call a host which have already connected with other, you will get a message box "Sorry, your friend is busy now!", and disconnect with him.
If you are a host and get a call when you have already connected with a partner, you will get a message "Get a connect from xxx.xxx.xxx.xxx, but you are busy now and disconnect it" in statusbar.
If you install NetTETRIS at first, and install ICQ later, maybe you can't find NetTETRIS in ICQ's user menu. You can reinstall NetTETRIS for appear it in ICQ's user menu.