Hey guys, I'm new to this website as well as Python and well, programming in general. Anyway, I would like some feedback on this program I wrote, its purpose is to take a credit card number, which the user inputs and determine whether it is a valid or invalid credit card number. I would like to know how I can improve my code, what I should have done differently and any other advice i could get, thanks!

def getEveryOther(creditCardNum, lst):
    for x in creditCardNum:
        lst.append(int(x))

    length = len(lst) / 2

    while length > 0:
        length = length - 1
        firstEveryOther = lst[-2::-2]
        secondEveryOther = lst[-1::-2]
        return firstEveryOther, secondEveryOther

def addFirstNums(listOfNums):
    y = 0

    for x in listOfNums:
        multBy2 = x * 2
        if multBy2 >= 10:
            newDig = str(multBy2)
            newDig = int(newDig[1]) + int(newDig[0])
            x = newDig
        else:
            x = multBy2
        y = x + y
    return y

def addSecondNums(listOfNums):
    y = 0
    for x in listOfNums:
        y = x+y
    return y

def checkIfDivBy10(sumOfBoth):
    if sumOfBoth % 10 == 0:
        return True
    else:
        return False

def checkCreditCardNum():
    creditCardNum = raw_input("Enter a credit card number: ")
    if len(creditCardNum) >= 13 and len(creditCardNum) <= 16:
        lengthCheck = True
    else:
        return creditCardNum, False

    if lengthCheck == True:
        if creditCardNum[0] == '4':
            return creditCardNum, 'Visa'
        elif creditCardNum[0] == '5':
            return creditCardNum, 'MasterCard'
        elif creditCardNum[0] == '3' and creditCardNum[1] == '7':
            return creditCardNum, 'American Express'
        elif creditCardNum [0] == '6':
            return creditCardNum, 'Discover'
        else:
            return creditCardNum, False
    else:
        return creditCardNum, False

def askUser():
    checkAgain = raw_input("Would you like to check another credit card? ")
    checkAgain = checkAgain.lower()
    if checkAgain == 'y' or checkAgain == 'yes':
        main()
    elif checkAgain == 'no' or checkAgain == 'n' or checkAgain == 'q' or checkAgain == 'quit':
        return None
    else:
        askUser()

def main():
    creditCardNum, creditType = checkCreditCardNum()
    lst = []
    if creditType == False:
        print creditCardNum, "is an invalid credit card number."
        return False
    firstEveryOther, secondEveryOther = getEveryOther(creditCardNum, lst)
    firstNums = addFirstNums(firstEveryOther)
    secondNums = addSecondNums(secondEveryOther)
    sumOfBoth = firstNums + secondNums
    validOrNot = checkIfDivBy10(sumOfBoth)
    if validOrNot == False:
        print creditCardNum, "is an invalid credit card number."
    elif validOrNot == True:
        print creditCardNum, "is a valid", creditType, "credit card."
    askUser()

main()

A nice effort!
You can simplify your first function ...

def getEveryOther(creditCardNum):
    mylist = []
    for x in creditCardNum:
        mylist.append(int(x))
    firstEveryOther = mylist[-2::-2]
    secondEveryOther = mylist[-1::-2]
    return firstEveryOther, secondEveryOther

... and call it with ...
firstEveryOther, secondEveryOther = getEveryOther(creditCardNum)

Another simplification ...

def askUser():
    checkAgain = raw_input("Would you like to check another credit card (yes, no, quit)? ").lower()
    if checkAgain[0] == 'y':
        main()
    elif checkAgain[0] == 'n' or checkAgain[0] == 'q': 
        return None
    else:
        askUser()

Thank you very much for your reply! I cleaned up my code based on your suggestions (after looking at my code, I'm not sure why I made my first function act like that) and fixed my main function because it wasn't performing as intended in every situation. I believe everything works now, here's the new code:

def getEveryOther(creditCardNum):
    lst = []
    for x in creditCardNum:
        lst.append(int(x))

    firstEveryOther = lst[-2::-2]
    secondEveryOther = lst[-1::-2]
    return firstEveryOther, secondEveryOther

def addFirstNums(listOfNums):
    y = 0

    for x in listOfNums:
        multBy2 = x * 2
        if multBy2 >= 10:
            newDig = str(multBy2)
            newDig = int(newDig[1]) + int(newDig[0])
            x = newDig
        else:
            x = multBy2
        y = x + y
    return y

def addSecondNums(listOfNums):
    y = 0
    for x in listOfNums:
        y = x+y
    return y

def checkIfDivBy10(sumOfBoth):
    if sumOfBoth % 10 == 0:
        return True
    else:
        return False

def checkCreditCardNum():
    creditCardNum = raw_input("Enter a credit card number: ")
    if len(creditCardNum) >= 13 and len(creditCardNum) <= 16:
        lengthCheck = True
    else:
        return creditCardNum, False

    if lengthCheck == True:
        if creditCardNum[0] == '4':
            return creditCardNum, 'Visa'
        elif creditCardNum[0] == '5':
            return creditCardNum, 'MasterCard'
        elif creditCardNum[0] == '3' and creditCardNum[1] == '7':
            return creditCardNum, 'American Express'
        elif creditCardNum [0] == '6':
            return creditCardNum, 'Discover'
        else:
            return creditCardNum, False
    else:
        return creditCardNum, False

def askUser():
    checkAgain = raw_input("Would you like to check another credit card (yes, no, quit)? ").lower()
    if checkAgain[0] == 'y':
        main()
    elif checkAgain[0] == 'n' or checkAgain[0] == 'q':
        pass
    else:
        askUser()

def main():
    creditCardNum, creditType = checkCreditCardNum()

    if creditType == False:
        print creditCardNum, "is an invalid credit card number."
    else:
        firstEveryOther, secondEveryOther = getEveryOther(creditCardNum)
        firstNums = addFirstNums(firstEveryOther)
        secondNums = addSecondNums(secondEveryOther)
        sumOfBoth = firstNums + secondNums
        validOrNot = checkIfDivBy10(sumOfBoth)

        if validOrNot == False:
            print creditCardNum, "is an invalid credit card number."
        elif validOrNot == True:
            print creditCardNum, "is a valid", creditType, "credit card."

    askUser()

main()

A simpler way to add up the first two numbers.

def addFirstNums(num_in):
    multBy2 = num_in*2
    y = 0
    ## convert to string and cut to two digits if more than two
    ## doesn't matter if one or more digits
    newDig = str(multBy2)[:2]
    for num in newDig:
        y += int(num)
    print num_in, multBy2, y


for num in [2, 6, 102]:
    addFirstNums(num)
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