I don't need a domain name. People can just target your IP address.
As XpertHamm0r kind of said, if you don't have ana public IP address dedicated to this server, you will need to set up port forwarding on your router so traffic destined for port 80 to your house will be redirected to your privately addressed server.
If this doesn't make sense to you, read up on NAT and how it applies to consumer Internet service.
As XpertHamm0r kind of said, if you don't have an IP address dedicated to this server, you will need to set up port forwarding on your router so traffic destined for port 80 to your house will be redirected to your privately addressed server.
What does one thing have to do with the other? You can not have a static IP address and not need to forward ports, and you can have a static IP address and still need to forward ports. They are separate states dependent on separate conditions.
I think you misunderstood me, which means the OP probably did as well.
Assuming OP is talking about running a web server out of his house, he very likely only has one IP address which serves his whole house, and traffic is redirected to individual devices via NAT(PAT).
If OP wants to allow outside addresses to initiate connections to the webserver, then some port forwarding is going to have to happen, as the server is going to have a private address, and the router will need to know to redirect port 80 (or whatever OP wants to run it on) traffic to that private address. This has nothing to do about static addressing, besides OP will need his server to have some static address.
If OP has two connections to his house, he can just have one connection (public IP address) for his server and not have to worry about port forwarding, because he won't be dealing with NAT.
@ OP: Anytime you have an outward facing machine like this it is good practice to put it on it's own sub net. This is a function of your router and what it does is prevent that machine from seeing any other devices at your site by putting that device on it's own mini-network. I would also suggest that you set your router to explicitly deny access to it's interface from this device through both wireless and wired connections. This one may or may not be practical and can easily become more trouble then it is worth from an administration stand point but it is still a good security practice to consider. Since this device will need an internal static IP anyway then restricting the IP range on that sub net might be something else to consider, but again this is one of those things that might not be worth the effort to implement since it really only throws up a road block in the event that another device tries to join that network.
There are some other good practices to consider, things like only running the services that the device needs to host your site and ensuring that all of the automatic updates for those services are set to Auto. But I'm thinking that the package that modoran suggested probably auto-configs a lot of that for you anyway.