I've seen many people asking this question over and over again and 1ce for all I'm making this tutorial that will let you connect to Internet in Ubuntu (and probably Mint Linux Too)

WARNING : It is quite possible that Network Manager may fail or act absurd due to bugs

So here are the steps :

WIRED

1)Go To The Networking Icon Just near The Date & Time , Right Click That Icon and Then Click Edit Connections...
   
2)A window will pop up titled Network Connections
Now here you can see your LAN Connection under Wired Tab (it will be somthing like Auto eth0

Note : If its not shown there then probably your network card is not detected
3)If your connection is just through Cable without any Dial-up option(aka the Direct Connection) then you are just ready to rock n roll but if u have a Dial-up connection that requires DSL to dial before connecting then you just need another few more steps .

Direct Connection

The Direct Connection users just need to set their IP settings that they can set clicking the Edit... button and then editing the IPv4 or v6 settings
Here is an Example :
   
Dial-Up Connection
The Dial-Up users must create a DSL connection in order to dial
a)To create a new DSL connection goto the DSL tab
b)Click on the Add button and then give some connection name say XYZ
   
c)Enter your username and password as provided by your service provider
d)You may or maynot give Service name (optional)
e)You may choose Availble to all users to make that connection availble for all users

Quote:Note : If some how your Network Manager fails to connect you may try the old method of terminal
For that open a terminal window and type sudo pppoeconf
Keep Hitting Enter Till you see a windows asking 4 Username (Pressing Enter After This Prompt you for Password)
Keep Hitting Enter till you are finished with this
pon dsl-provider will let you connect & poff dsl-provider will let you disconnect from Internet

WIRELESS

Those people who want to connect to Wifi Connection will be able to see all connections available automatically when they'll left click on the Network Manager Icon (near the date and time)
If you are not able to see ,you can follow the Step 1 of Wired Connection and then select WireLess tab

MOBILE

Frankly I've not tried this so I'll be really glad if someone comes up with couple of lines that will let users to easily connect to Internet using mobile (though IMO it will be almost the same )

Feedback & Suggestions Are Invited TO Make This Guide More Easier And Comprehensive....!!!

this tutorial must not be for ubuntu karmik koala users with broadcom wireless devices having problems with their wireless devices

karmic is worse
network issues galore in it
the gui for connection suckz
lets c wat v can get in lucid
& ill like to add its shameful on part of programmers that they havent sorted out the issues yet

^^Plz Mention you Ubuntu Version

It is simple to connect Internet in Ubuntu. First Go to System and then Administration. Here the networking option is given. From here you can set the Internet connection. You can edit the settings and change the Gateways from the above right side of the Display windows.

Network manager has improved considerably since Jaunty (9.04)

Michael next time you post a question do mention which distribution you are using.Also if you dont seem to get a quick reply here then we are always available on FB or Twitter