re andjac: possibly but the trains to headingley were never very regular from what i remember - ok slap me with a wet herring and call me a liar, according to Nat. Rail enqs web site you can get the 7.59 or 8.29 train from Leeds arr. Headingley (though it is bottom end of headingley = 10 minutes walk to town centre, so maybe the bus might be a better alternative).
EliPledge the walk from Leeds or from Pudsey to Headingley is around the same distance, i would say 30-45 minutes at least and not a very pleasant one as it's all main roads and inner city traffic. I would recommend getting the train to Leeds, then getting a train from Leeds to Headingley as andjac recommends (or getting the bus, whichever you choose)