What is the best way to split a string to get all the substrings by Ruby?

I'd write:

def split_word(s)
  0.upto(s.length - 1).flat_map do |start| 
    1.upto(s.length - start).map do |length| 
      s[start, length]
    end
  end.uniq
end

groups = split_word("stack")
# ["s", "st", "sta", "stac", "stack", "t", "ta", "tac", "tack", "a", "ac", "ack", "c", "ck", "k"]

It's usually more clear and more compact to use map (functional) instead of the pattern init empty + each + append + return (imperative).

def split_word s
  (0..s.length).inject([]){|ai,i|
    (1..s.length - i).inject(ai){|aj,j|
      aj << s[i,j]
    }
  }.uniq
end

And you can also consider using Set instead of Array for the result.

PS: Here's another idea, based on array product:

def split_word s
  indices = (0...s.length).to_a
  indices.product(indices).reject{|i,j| i > j}.map{|i,j| s[i..j]}.uniq
end