How to access a personal home server?

The server would probably have a web interface like your router does.

A Server is simply a "switch" on a network that manages & directs incoming & outgoing IP traffic to optimize efficiency… If you are the ONLY client on the network at your house, you'd be COMPLETELY wasting your money installing a Server because you wouldn't be DEALING with any other traffic!

Save your money and spend it on some education instead!

" how do you access it to like turn the minecraft server on "inside"? I"

With a program on a computer with a screen. I hate to give such a vague answer, but that's it, and there's so many tools to do it, going further down is rather hard.

" If anyone can find a tutorial on how to setup a personal home server for minecraft that would be great!"

It's easy, use Google.

If you're going to buy an actual server, then yeah, some servers have KVM built into the motherboard, or some sort of management interface, but either way, especially since you will have physical access to it, it never hurts to have a good old keyboard and monitor or TV nearby.

#1 Install Server OS if necessary And update it until it won't update anymore.
#2 Minecraft runs on Java, so you'll need to install the Java (JRE) if necessary. For Windows that's easy enough, ya download it from Oracle's site. For Linux, depending on your distro you can find pretty good instructions by googling nowadays (My 'server' is running Linux Mint, a Ubuntu derivative, (great for Linux newbies) so I google 'Java webupd8 ppa' and follow the instructions.)
#3 Download the minecraft server program (on the minecraft.net web site) and put it somewhere where you can get to it.
#4 (IF you want your friends to be able to access the server from the internet) Now you'll need to make sure to forward connections to port 25565 to the server that will be running Minecraft. You can do this by logging into your router or gateway and there's a management screen (usually under a tab named something like 'applications' or 'port forwarding') containing a list of any ports and the IP addresses they are forwarded to. You can find the (internal) IP of your Minecraft server by finding the routing table screen on your router, or somewhere in the network connection properties on your server. Unless you're running any more services on that server, no other connections to any other ports should get to that box. If you're putting your server on the internet, I suggest you don't skip this step, for security reasons.
#6 You should be ready to start the server. On Windows you just double-click the exe and let-er rip. On Linux, open a command prompt, "cd" to the directory or folder that the minecraft server is in, and enter the command to start the server. I.e. Something like:

java -Xms2048M -Xmx2048M -jar minecraft_server.1.8.8.jar nogui

#7 the first time you run it, it will automatically shut down and create an EULA.TXT file. You have to open the file in a text editor and change 'false' to 'true' in the file. Then start the server again and it should say it is successfully running.

Any problems accessing the server at this point (especially from the internet) can probably be attributed to networking equipment between the server and the street that is blocking connections to that port. It's usually not the firewall.