Triumph, dudes! The key was really seeing how it worked on the much simpler math of finding a certain number of odds. This works now! Still probably a million times clunkier than some, but I've never programmed before in my life and using what we've learned so far I got to this point. I've documented it a lot so that y'all can see what I did and why. Also, I apologize to elz's inbox, where all my edited comments full of code probably ended up.

# primes
# AKA sleep is for the weak
# This script will calculate the nth prime number

primes = [2] # This is a list called primes, and its first item is 2
counter = 1 # Because 2 is the first prime and your list already has 1 item.

print ("Let's find the nth prime number. Please enter a postive integer: ")
answer = raw_input()
nth = int(answer) # The user enters the answer N. To do math with the answer, you have to make it an integer.
prime = 3 # Start at 3 so you don't have to deal with the fact that 2 is the first prime.

while counter < nth: # Until you reach N, follow these instructions:

     if nth == 2: # So you don't have to deal with 2 being the first prime
          primes.append(3) # Make sure you keep your list up-to-date otherwise nothing else will work
          print ("The ") + str(len(primes)) + ("nd prime number is 3.") # Concatenating strings & integers is fun!
          break # I don't know if this is necessary, but it gets you out of the loop.

     elif 2 < prime and prime % 2 == 0: # Here's where the real work starts. If the potential prime is even:
          print str(prime) + (" is even. It doesn't go on the list.") # You don't go further.
          print ("We have found ") + str(counter) + (" prime numbers. Let's keep going.")
          prime = prime + 1 # Having dealt with one case, make sure you increase the iteration

     elif 2 < prime and prime % 2 != 0: # If the potential prime is odd:
          print str(prime) + (" is odd. Let's keep working with it.") # There's more to do.

          factor = 2 # Start with a factor of 2 because primes are divisible by 1.
          while factor <= prime*0.5: # Once you get to half the number, the rest of the factors are mirrors.
               if prime % factor == 0: # If it's divisible...
                    print str(prime) + (" has a factor. It is not prime.")
                    prime = prime + 1 # Increase the iteration but not the count of prime numbers
                          # (You haven't found any prime numbers yet.)
                    break
               elif prime % factor > 0: # If it's not divisible...
                    print str(factor) + (" is not a factor. Let's keep going.")
                    factor = factor + 1 # You've tried one factor, now try the next.


          if factor > prime*0.5: # You need to know that all your tests failed.
               # But if you get out of your loops every time a test was true,
               # then if your loops are good,
               # so having checked all possible factors should be enough.
               primes.append(prime) # You have found a prime number! Add it to your list.
               if len(primes) == int(nth) and len(primes) == 3: # If you've reached N, print it out.
                    print ("The ") + str(len(primes)) + ("rd prime number is ") + str(prime) # This is just fancy to get the ordinal correct.
                    break
               if len(primes) == int(nth): # If the number of items on your list is equal to N, then stop.
                    print ("The ") + str(nth) + ("th prime number is ") + str(prime)
                    break
               else: # If you haven't reached N, keep going.
                    print ("We have found ") + str(len(primes)) +(" prime numbers. Let's keep going.")
                    prime = prime + 1 # Increase the potential prime by one.
                    counter = counter + 1 # Since you've found a prime, increase the count by one.

if nth == 1:
     print ("The 1st prime number is 2.") # This helps deal with users who enter 1 as N. (Very funny, users. Not.)
if nth == 1000: # To shorten the program run time, comment out all that printing and just leave this one.
     print ("The ") + str(nth) + ("th prime number is ") + str(prime)