You can either run the server yourself, and leave your computer on 24/7, or buy a server. There are plenty of options, look under Minecraft server forums. By the way, I recommend not to download any contents from the link above. It's probably unsafe. All the information needed is stored on the forums, and you have no need to take risks.
I would use bukkit if I where you ( www.bukkit.org ). You have tons of plugins to choose from. The instructions are in the donwload page, just go here: http://wiki.bukkit.org/Setting_up_a_server
There are some instructions, just follow them. Just run it and leave your computer on. That's pretty much it. As for the players, you can announce your server here, in the forums.
For the official launcher ( The one made by Mojang ) go here: http://www.minecraft.net/download .
Now, if you want people to connect your server, you'll have to forward your ports http://portforward.com/english/routers/port_forwarding/routerindex.htm
Find your router there ( Just examine your router, and check the model ) and find Minecraft, then follow instructions.
Or you can use Hamachi. You just have to create a network or join an existing one, and invite those who you want to play with you, and they'll be able to join.