The manual for test has some helpful info. It's available with man test.
Operators for text strings
   o STRING1 = STRING2 returns true if the strings STRING1 and STRING2 are identical.
   o STRING1 != STRING2 returns true if the strings STRING1 and STRING2 are not
     identical.
   o -n STRING returns true if the length of STRING is non-zero.
   o -z STRING returns true if the length of STRING is zero.
For example
set var foo
test "$var" = "foo" && echo equal
if test "$var" = "foo"
  echo equal
end
You can also use [ and ] instead of test.
Here's how to check for empty strings or undefined variables, which are falsy in fish.
set hello "world"
set empty_string ""
set undefined_var  # Expands to empty string
if [ "$hello" ]
  echo "not empty"  # <== true
else
  echo "empty"
end
if [ "$empty_string" ]
  echo "not empty"
else
  echo "empty"  # <== true
end
if [ "$undefined_var" ]
  echo "not empty"
else
  echo "empty"  # <== true
end