We have a large bank of possible Crosswords answers - approximately 60,000 words and growing, and an even larger bank of clues so that we have options to vary which clues we choose.
We try our best to include spellings which are universal, and clues which are culturally universal too. We do have some acronyms ( LASER, SCUBA, NASA ) and some initialisms ( FBI, NYC ) in there too.
Each of the words is ranked by how well known it is - which we work out from the 'frequency' of its usage in a large collection of English language books. The words are rated from extremely common through to extremely obscure.
We start each puzzle with a predefined grid - each of the gaps has to cross other words, and we do our best to make it cross as often as possible. The places where two words meet is sometimes call a 'check'. In the case of a word that crosses others several times, we might say that it has been checked three times. It should be possible to go from any word to any other in the grid via open spaces - that means there shouldn't be any orphaned words or sections. For good aesthetic reasons, the grid should also be rotationally symmetric too.
The grids we use are the 'British' style which means that about half of the cells in the grid have a letter, and half have a 'blank', which spreads out the words a bit. We find that the more packed 'American' style crosswords (like the excellent New York Times) tend to have a lot more initialisms and fractions of phrases which don't then translate as well to an international audience.
We then fill in the grid a word at a time. We work through putting in the bigger words (the most checked) first, and then with those in place work on fitting in the smaller and smaller words until the whole grid is complete. It's very very rare to get this right the first time and we always have to backtrack many times (sometimes thousands!) and remove some before trying again with different words.
We make sure that the words we choose haven't already been used in that puzzle, and also since we are aiming to build a puzzle of a particular difficulty, we also look at the obscurity of the words too - a hard puzzle is allowed and encouraged to have far more obscure words than the easy or daily puzzles.
You'll notice if you look very carefully that the letters in words that are checked - that is, shared between two words - are often the more commonly used letters. This is because it's easier to find another word crossing that point with one of the most common letters ( ETAOIN SHRDLU ) than more awkward letters like XZCBFQ.
We have a particular fondness for the word 'AVOCADO' which when used one way can cross on the A O A O (very easy to fit in) and the other way ( V C D ) is much harder to fit in.
When the whole crossword grid is filled in, the total difficulty is calculated based on the average obscurity of the words.
We then work on adding in clues to each word, and that normally means we choose from a range of possible clues. Sometimes we choose from one we've used before, and sometimes we create a new one, which just adds to the bank of clues. Most of the clues are either simple general knowledge or synonyms, but sometimes we like to include anagrams, and the occasionally slightly cryptic clue too, just for more variety!
Once that's complete, the puzzle gets stored in a database, and will later be checked by another of us for proofreading, which is checking that all the clues seem reasonable, and that there's nothing too rude if you read out some of the answers or clues in order! (Yes, this has happened, no we're not telling! ) There's a final opportunity to either discard the whole puzzle or (preferably) change or fix any of the clues to make it better.
Finally the 'ready' puzzle sits waiting to be included in either a pack or as one of the daily or weekender puzzles. We usually try to keep several hundred puzzles ahead for each of the categories.
Puzzles are selected for the dailies as long as they are within the right range of difficulty, and also don't contain any clues or answers which have been used in a puzzle within the last few days. We try to keep it at least three weeks between repetitions, and more if we can, but sometimes that isn't possible within the current bank of puzzles so there may be a few 'collisions' along the way. A few of our more eagle-eyed regular players notice these, but as we create our own puzzles we hope you'll forgive the occasional answer that's a bit easier than usual because you've remembered it from a recent puzzle!