I want to lan my connection with my neighbours computer.what should I do for it?I would like to connect through wire.how to set up the network connection.There is only two computers to be connected together.So tell me about peer to peer connection.

Fastest and easiest is to buy Cat5 Cable and crimp it together yourself. Make sure you buy cable that will be able to handle weather conditions (it is a little bit more expensive tho). I bought 1000 feet of Cat5 (inside only) at Home Depot and paid under $100. Next thing you need, naturally is 2 Network Card or you might have them on your mainboard.
To save the trouble of buying a crimp tool you should get Cat5 Jacks they have the color markings already on them, you just have to make sure that you use crossover if you do not want to buy a hub/switch (crossover is only required if its from one NIC to another). If you share internet that way and one of you has a router where both are plugged in, you don't need the crossover though. Anyway the color markings can be found here Cat 5 COLOR Code Standards
If you have to wire outside to another house (you didn't mention if it is a appartent or not)
You might be cheaper off to go wireless. Oh and if you use the jacks each one of you needs a small patch cable that goes from the end of the jack to the nic.
All off the above metioned material is available at home depot (at least in canada don't know about the states)
I attached a picture off the cat5 jack for reference.

They use Leviton "Quickport" down here(Home Depot). I like better because like the one in picture, You cannot fit 6 in single gang quickport plate. Leviton you can.
Excellent link and info by benreilly.