I was wondering something, I checked my network services and I see that I have finger running, how can someone use this to hack into my computer and how would they go about doing it? Thank you for your help.

They can use it to gain knowledge of user & system info. Any available information to a malicious user is good for them, even if all they know is that you run an rpm-based system. At least it gives them something. Read a couple Certified Ethical Hacking books and you'll get what I'm talking about.

As for how they'd exploit it, I believe their is a rule about posting info on how to crack into computers, and even if there wasn't, I can't predict how you and everyone else in the world reading this would use that information. All I can say is read up on as much hacking/cracking books and senarios you can, understand what runs on your system and how that effects the system, implement the most paranoid and rediculous security measures possible and then lessen the security if clients can't use the system in the ways they were meant to.

You don't need to run finger or offer the service. However, if you are behind a NAT router and don't have port 79 (both tcp/udp according to /etc/services) open, then this service is just available on the LAN. On the other hand, if this is your only computer, then there is absolutely no reason to offer it. For a host in the DMZ, offering services to the internet, you absolutely want to disable the service and block the port.

how can someone use this to hack into my computer and how would they go about doing it?
The finger daemon is an interactive service, it will accept input and will return output. The input must conform to rules. If these rules can be broken you can try to make it do stuff. If you for instance can force the application to accept malformed or too much input that it starts to execute commands you embedded in your input, then you can try to execute commands as the owner finger runs as. There are safe(r) versions of finger around and even ones that return bogus information. AFAIK about the only thing that still uses finger is IRC. As the rest said in general you won't need it. If you need it you would know ;-p

check the story of Morris Worm.