I use to love playing spinners and faster guys but now with time I have found that I struggle against spinners...most notably 2 seasons ago if I was going well and a spinner (Leggie) came on I was a guranteed wicket... so after doing some work on what works for me and what doesn't i ended up with....
Watch the flight, not the turn, if its going to land anywhere close to where i can get to (including stepping out) then I am going to make it there and either smash it out, play it for a single (rarely) or block it...its a lot easier to block a full toss/half volley then a turning spitting spinner...if its going to be a short one then i have lots of time to play it off the pitch...really bothers them too if they know you are willing to step out...
One thing that i have noticed i did and lot of others do is when they step out is most of them are moving down the leg side direction regardless of where the ball is, always move towards the ball to meet it either on the bounce or full toss...
I haven't swept a spinner in 2 years now, have had a lot more success against them with dancing down the track...