How to invite people to a single player world in Minecraft?

First you have to open your world and then press e which will open options. Then click open to lan on the right hand side. Then choose your preferences. Do you want the world to have cheats or be in creative? Anyway, after that your friend should go into the title screen and click multiplayer. It should say lan worlds and if you two are in the same network, it should work, and your world should pop up on his screen.
please note that the lan world only works if the host is on the world, and if the host leaves, the guest who came to the world will automatically log out. The guest must log out first to avoid glitches and/ or bugs. If you log out of the world and log back in, you must open the options again and set the lan preferences. It will not stay there after you leave the world.
is that too much instructions? Oops.

You will have to make a minecraft server and not a LAN server, as audrey said.

First go to the minecraft download page and download the minecraft server. Then put it in a folder and open it. Follow the instructions and after that you will have to port forward your minecraft server. Watch a instruction video on how to do that. There's tons of them on youtube. Then for you to join it you will have to join your local IP. Its something like 192.168.2.1. Your friend would have to join your public IP. Just google "what is my ip" and she will have to join that one.

Since that requires some experience to do, i will recommend using hamachi which is easier to use. Just search for a tutorial and you're done.

To put your world into your server, do to the start menu and type in %appdata% then click enter. Click.minecraft -> saves then click on your world. Copy the files inside and go to your server folder. Delete the folders in "world" and replace them with what you just copied. Open the minecraft server and you're done.