Well, it all depends. If you bought the server, stuck it in your closet, then yes, you will still need an ISP. You have to have some way to hook into the Internet. Basically, you just need an IP address, which an ISP assigns. Once an IP is assigned, then you can just type in that IP into a web browser and it should connect to your server (of coruse, you've got to set-up some stuff on the server...).
However, you can go the easier route and buy a server from a company. This company, for a monthly fee, would give your server internet access and have the software set-up on it. A company that does this can be found here (I'm not recommending them, I've never used them):
Now, I'm not a Linux expert (I"m sure their is some kinda bootable server off of a CD or something), but I do know this. You will need an OS, like Windows or Linux. Then you would need some kind of server software. You can use Microsoft IIs for this or Apache Web server (www.apache.org). I would recommend Apache b/c I have used them, its open source (so well documented), their is plenty of help, and it wasn't too hard (digging through the config file is a little daunting at first).
If you want to see what it's like running your own server, just download Apache and have it run locally! You can act like it's on the web, it's just you are the only one that can access it. I do this on my local machine so I can preview my changes (I use SSI) without uploading it. I also like to write PHP scripts w/out an internet connection, so I just test em using Apache.