Using Ethernet (ADSL or PPPoE), to connect to the internet is relatively easy with Mepis, because when the distribution, begins to run, it tries to detect all the network interfaces in the computer.
So after the whole boot process has finished and you have passed the login screen (where you have entered the apropiate password), you will be looking at your desktop.
To finish setting up your internet connection, you must click: Kmenu > Internet > Connection > ADSL/PPPoE configuration, and follow the different screens, where you will be asked for some ISP information (like your username and password). Complete that section and a few seconds later, you will be surfing the Internet.
Here is a link to networking basics. Taken from the MEPIS wiki. http://www.mepis.org/docs/en/index.php/Networking
Here is some stuff you can type into knosole.
ifconfig - main configuration utility for network interfaces. Please read man ifconfig for full documentation.
ifup interface - bring up the specified interface. For example:
ifup eth0 - command that brings up the ethernet port
ifup wlan0 - command that brings up the wireless port
ifdown interface - the opposite of 'ifup' it brings down the interface.
iwconfig - wireless network connection utility. Check out man iwconfig for full documentation. Here are a few useful iwconfig commands (NOTE: your wireless card could be referred to by one of several names on your system. eth0, ath0, and wlan0 are common. Wherever you see one of those, substitute your adapter's name):
iwconfig - by itself, iwconfig will display your wireless status
iwconfig eth0 essid any - this command connects eth0 to any AP in range
iwconfig wlan0 essid foo - connects wlan0 to AP with essid "foo"
iwconfig eth0 key off - clears out the WEP key
iwconfig ath0 key 12345678901 - sets ath0's WEP key to 12345678901
iwlist - another wireless ethernet utility. See man iwlist for complete information. Some useful commands:
iwlist wlan0 scanning - shows properties of all wireless networks within range of wlan0.
iwlist ath0 bitrate - shows the current speed of communications on ath0.
Hopefully this will get you on the right track.