Richmond is a smaller airport than Chicago, so it shouldn't be too hard to navigate. When you arrive your priorities are (in this order):
1) Verify you don't have anything sharp in your carry-on, or large amounts of liquid. All liquids/gels in your carry-on must fit into a small zip-lock bag. Anything questionable, put it in your checked bag.
2) Find the line for your airline to get your boarding pass and drop off your bag. You'll need a driver's license or other ID for this part. Some airlines have an online check-in option which allows you to go to a (usually shorter) "bag drop" line instead, but that depends on the airline and the airport. I haven't been to RIC. Plan to wait in this line for 15-20 minutes or so (although it can be much shorter or, occasionally, longer).
3) Once you have dropped off your checked bag, find the security checkpoint. Make sure it's the right one----sometimes there are multiple checkpoints accessing different gates. The security line will often be another 15-20 minutes.
4) To streamline security, just make sure:
a) If you have any liquids or gels in a zip-lock, they go in the bin.
b) If you have a laptop, it goes through separately.
c) Everything in your pockets goes in the bin.
d) If you have a belt or other article with metal parts, bin.
e) Shoes go in the bin or separately.
f) Hang on to your boarding pass! They probably checked your ID for the last time further back in the security line, but you still need that boarding pass when you go through the metal detector. Don't put it in the bin.
g) Don't make jokes about bombs. TSA personnel do not have a sense of humor they're aware of.
5) Now all that's left is to find your gate. There will be prominent signs directing you to the proper concourse, but keep an eye out for food along the way---especially when you're early, a place to get a bit of breakfast is a good thing.