Sarah Trowbridge's Random Menu Generator. Note that the met the primary requirements were met for this project and I attempted some of the optional enhancements but the enhancements are incomplete. I am going to return to this at a later time to complete it.

RMG_ST.rb

puts "Welcome to the internet's most random food generator!"
puts "How many dishes can we tantilize you into reviewing today? Select a number between 1 and 10."
number_of_dishes = gets.chomp
if number_of_dishes.to_i > 10
  puts "That's a bigger number than the number of dishes our chef can cook! Please select a lower number."
#Need to figure out a way to have the program not continue if they select a larger number than 10.
elsif number_of_dishes.to_i >= 1 && number_of_dishes.to_i <=10
  puts "#{number_of_dishes.to_i} dishes, excellent choice!"
else
  puts "That's not a number, silly. Let's go with 8 dishes!"
  dishes = number_of_dishes.to_i
  dishes = 8
end
#Note - I haven't figured out a way to incorporate the users input and generate the below based on their response.
#I also haven't figured out to how to ensure that the user does not see repeating options.

adjective = ["steamy", "stinky", "smooth", "slimy", "sweet",  "succulent", "aromatic", "flaky", "slippery", "bountiful"]
cooking_style = ["chilled", "crisp-fried", "burnt", "plucked", "skinned", "mushed", "sizzled", "smoked", "flash-fried", "frozen"]
food = ["squid legs", "octopus eye", "salmon scales", "shark fin", "sea snail", "baby star fish", "seaweed", "tuna sandwhich", "clam bake", "turtle head"]
numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

adjective.shuffle.delete(adjective)
cooking_style.shuffle.delete(cooking_style)
food.shuffle.delete(food)

puts "Today's delicacy will be..."

numbers.each do |n|
  puts "#{n}. #{adjective[rand(10)]} #{cooking_style[rand(10)]} #{food[rand(10)]}"
end

Per your comment on line 6, you could utilize a while loop which could allow you to repeatedly ask for user input until the user entered a valid number

In your else on line 9, it seems like line 11 is not necessary since your program will ignore the user-input value and reset it to 8

Take a look at the docs for the shuffle method. I don't think it is shuffling it the way you think it is. I think the one you would ultimately want is the shuffle!. We haven't really talked about the differences, but the docs should explain it a bit: http://ruby-doc.org/core-2.2.0/Array.html#method-i-shuffle

Nice job with your final each loop. Hopefully now you see how you might be able to use a range rather than create this separate numbers array which would do the same type of thing for you.