Are there any tips/shortcuts/memory aids for learning how to decline numbers?

Speaking about Russian cardinal numbers, there are several guidelines that will help you remember how to decline them.

One, Two

1. The only cardinal numbers that change by gender are один/одна/одно and два/две, plus compound numbers that end in 1 or 2 (such as 21, 52, 171, 142). The rest of cardinal numbers does not change by gender.

2. The numbers один/одна/одно act like the pronoun этот, agreeing with nouns in gender, number and case.

Two

1. The number 2 has the same masculine/neuter form in the nominative два. The feminine form is две.

2. Have to memorize the declensions for два:

   Nominative: два/две
   Genitive: двух
   Dative: двум
   Accusative = Nominative or Genitive
   Insturmental: двумя
   Prepositional: о двух

Three, Four

1. Have to memorize the declensions for три:

   Nominative: три
   Genitive: трёх
   Dative: трём
   Accusative = Nominative or Genitive
   Insturmental: тремя
   Prepositional: о трёх

2. Have to memorize the declensions for четыре:

   Nominative: четыре
   Genitive: четырёх
   Dative: четырём
   Accusative = Nominative or Genitive
   Insturmental: четырьмя
   Prepositional: о четырёх

Five through Thirty

1. Numbers 5-30 ending in a soft sign (-Ь) act like the noun тетрадь
   

Fifty, Sixty, Seventy, Eighty

1. Compound numbers 50, 60, 70, 80 consist of two parts (e.g. пятьдесят = [пять+десять]). Both parts act like the noun тетрадь (e.g. пятидесяти, пятьюдесятью)

Forty, Ninety, One hundred

1. The numbers 40, 90, 100 end in -A in all cases, but Accusative = Nominative.

One thousand

1. The number 1,000 acts like the noun задача

One million

1. The number 1,000,000 acts like the noun стол