I agree with you CD. That's a great place to start in learning how to work on guitars.
The easiest way is to take the nut in with you. If the guitar is an inexspensive acoustic steel string, it's a fairly straight forward project. Most of them are relatively standardized in size - take off the strings, clean up the slot/shoulder CAREFULLY and reglue. Restring, have fun
As much as I love Guitar Center, this is when the smaller shop is probably a better place to go. Many of them will have a tech on hand... or even the sales people will know enough to get you what you need.
I'm always amazed how easy it is to work on guitars - acoustics and electrics. I do a lot of woodworking, automotive, home DIY stuff - so taking apart my guitars and tweeking/fixing them has become a natural extension.
Just take your time, plan on several evenings -
Day 1: take off the nut/clean up the spot
Day 2: go to the guitar shop and get the new nut (and strings)
Day 3: polish up the body, oil the neck, tighten the tuners bolts (there will be at least one loose), carefully glue the nut on - leave the guitar set over night - don't fiddle with it, pick it up, etc. until the next day.
Day 4: Restring and have fun!
Tension rod - again search the web. Tighten/Loosen to get the proper bow. You can use automotive
spark plug feeler guages to check for proper clearance.
If it has an adjustable bridge - Set the string height/intonation: search the net for neck adjustments for your exact model/style of guitar -or- for the style of guitar that yours seems to fit (most acoustics will be similar). Sit with a beer and a GOOD electronic tuner and plan on about an hour for your first time making adjustments.
It's amazing how playable even the trashiest guitar can be set - it may not last that way if there are other problems however.
Have fun!