How can i connect PC to PC using LAN if both computers are using Ubuntu 10.10?

The easy way is to use a router

Get a basic router

Plug it in

Plug the two computers into LAN Ports (leave the WAN Port alone). Use Ethernet Patch cords

The router will assign IP addresses and you are connected

Another way is to use a switch.They are a little cheaper

Get your switch

Plug the computers into the switch using patch cords

On each computer assign an IP address and network mask

example Comp 1 - 192.168.0.10 - 255.255.255.0

Comp 2 - 192.168.0.20 - 255.255.255.0

The last way would be to use a crossover cable. (costs almost as much as a switch)

Plug the cable into each computer

assign IP address and Netmask same as for a switch

Have fun

FYI - the answer above is incorrect. You cannot use two wireless cards in "ad hoc" mode. They don't work that way

two ways. This one is the cheapest but it can be unreliable. Its with a crossover cable. It will connect both networking devices directly to each other by wire and the wire has swapped RX and TX wires on one end. The other option is to use a HUb/Router/Switch and two straight patch cables.

If you mean offline mode which means no internet this is what it is. It will be a simple network.

but the ethernet adapters must be seen by ubuntu and being known to work.

This can be done by two wireless cards in Adhoc mode. But in my experience with linux the pc had to be online to the internet to grab and install drivers for the wireless cards. I never used wireless cards in adhoc but I would assume linux has some walkthroughs for it.