What are good tips for playing the endgame in Scrabble?
There's a huge amount of information out there about Scrabble end-games - far more than I can summarise here - but most of it concerns two-player games. In those situations, it becomes possible to plan out the last few moves with a great deal of accuracy, since once the tiles are gone from the bag you can work out exactly what is on your opponent's rack. The key becomes maximising the points differential between you: so a 5 point move where the best response is 10 points would be preferable to a 10 point move with a possible response worth 20 points. You also need to factor in the letters that might be left on your rack at the end, since these tiles are worth double to your opponent (once when they are subtracted from your score and again when they are added to theirs).

In a 3 or 4 player game, as you describe, it is much harder to control the flow of play and work out what the other players are going to do. Therefore, it's much more about just maximising your score on any given turn. Still, there are a couple of things you can do in the endgame to help your chances:


Get rid of any high-scoring tiles from your rack as a priority.
Go for longer words if possible so that you can be the first to empty your rack.
As @Becuzz suggests, try not to leave any blatant double- or triple- word opportunities for the player following you.
If the bag is empty and you can't see the Q, you know one of your opponents has it, so try to block any tempting spots they could play it out.


Depending on the situation, some of these may be mutually exclusive, so you need to make a judgement call on which is a priority. E.g. if you have six tiles and an opponent only has two left, they will probably be able to clear their rack next go, so your priority should be to get rid of any high-scoring tiles from your rack.