Palm reading, as far as I'm concerned, is a load of crap.
Tarot reading depends on how you are viewing it.
IMO (and that of anyone scientifically inclined) it doesn't tell the future, because that's just stupid.
However I do own a few tarot sets, and find them very useful when I'm struggling to concentrate on a problem. As far as I am concerned, I know the order of the cards, I know the meanings of said cards, and I know the meanings of the different positions. Most of this knowledge is subconscious of course. So when I shuffle the deck, I subconsciously know where I'm placing the cards. And am therefore answering my own questions.
Of course for this to work I need to know all of the above and be the one doing the shuffling. Plus it has to be an already organised deck.
But then I still have to bear in mind that I am going to read what I want into the cards. So still have to take it with a pinch of salt.
The reason so many people get "accurate" readings is a combination of the above two thoughts. (Most people know the general idea behind the major arcana at least, and the main card layouts)
The other thing is cold readings.
Personally, I'd recommend buying your own deck. Or, even more simply, use a normal playing deck and familiarise yourself with what the different suits are usually connected with (eg. hearts = love/relationships), and the numbers (eg. 1/ace = complete, full)
That way you'll get as close as possible to what is already in your head. If the answer isn't already in your head, then there's no way anything like tarot will ever help you.