Well first of all welcome to Tamatalk! I hope you enjoy yourself here!
As for your question,
You cant connect with other people on the internet via the Tamagotchi....but you can connect to the website and type in passwords to get items you can either buy or get as a souvenir!
Heres the link:
TAMATOWN
If you have any questions regarding the site PM me or post it here.
Good luck!

Itachi
EDIT:
How to connect:
There will be an icon that looks like a heart that will allow you and another V3, V2, V1 owner.
To connect with a V3 hit the B button (Middle) on "Ver.3".
For a V2 or a V1 hit the B button on "Others".
This will bring you up to a screen saying the following:
Game
Present
Visit
Game:
When you go to "Game" you will play randomly an assortment of games you randomly win.
You dont have to do a thing!
The winner of the game will recieve gotchi points that will increase if you both donate a certant ammount of gp to the king.
Present:
When you go to this your pet will go to the other Tama's screen and hand him/her a random present!
(Mostly food but wont refill anything)
If it is a bad present the and the Tama that was the giver of that should be given an timeout if acts wierd afterwards.
You can also wrap presents instead of just giving random ones.
To wrap simply go to the book icon and select present from the menu.
Then after that select the item you wish to wrap and connect to them with present.
If your Tama is the giver then the reciever should get the present you wraped!
Visit:
Nothing much to it besides the fact that either yours or the other Tama's pet that you are connecting to, will visit your house and do random things....Like dance.
Well good luck and I hope this FAQ has helped you!