Given that it's a hangman game, I assume you are trying to see if a single letter is contained by a given string - so equalsToString: wouldn't be what you want.
Instead, probably better to use rangeOfString:options:
if ([randomString rangeOfString:self.textfield.text options:NSCaseInsensitiveSearch].location != NSNotFound){
// Do stuff for when the letter was found
}
else {
// Do stuff for when the letter wasn't found
}
Also, as was pointed out by Patrick Goley, you need to make sure you're using the textfield.text value to get the string from it. Same with storing the initial word you'll be using as the hidden word.
There are also a couple of other minor code issues (semicolon in the function header, for example) that you'll need to clean up to have a functioning app.
Edit: Made the range of string call actually use the textfield's text, and do so case-insensitive (to prevent false returns when a user puts a capital letter when the word is lower case, or vice-versa). Also included link to documentation of NSString's rangeOfString:options: