I am not sure why nobody will give you a straight answer - it's a simple enough question.
Download the server http://mirror.technicpack.net/Technic/servers/tekkitlite/Tekkit_Lite_Server_0.5.7.zip Extract in to a directory and take a look at server.properties (open with notepad, notepad++ etc.) The only option you will probably want to mess with here is the server name, world name, white list etc. (if you enable white list you will need to add the player names to the whitelist file that will get created). Run launch.bat and let it generate the world etc. at this point the server is up and running. If you are running on the same machine as your MC client then launch MC and select Multiplayer and just connect to localhost (you don't need to add the port unless you have changed from the default).
If your friend is in the same house/dorm/school etc. then he will need your internalIP address. To get that just open a command prompt and type ipconfig and get the IPv4 address (typically unless you have changed the default it will be 192.168.1.???).
If your friend is not on the same network you will need to do what's called port forwarding on your router. This will vary depending on the router you have. Take a look at http://portforward.com/routers.htm for your router and follow the guide. Essentially what you are doing is opening the Tekkit Lite server port on the router and forwarding it to your internal IP address. Your friend will need to connect to your public IP address, which will be dynamic unless you are paying for business internet or your ISP has provided a static so be warned that it could and probably will change in the future. However just head to http://www.whatismyip.com to get your public address. Give that to your friend and as long as you have everything setup correctly he should be able to connect.
You may need to add an exception to your firewall to. This is all assuming you are running on a windows platform.
One thing to note though, unless you have a pretty decent computer running the server and client on the same machine will eventually cause lag etc. but it's a free solution so you can probably live with it. I run both on my machine (4 GB for the server, 8GB assigned to the MC client) and it runs pretty well with hardly any lag.
Hope that helps.