Right, lets have a look at this new 'magic' psychic phase! First of all, the book gives a basic run down on psykers and how they work, mastery levels etc. The first change is that if your psyker generates all of it's powers from the same discipline, they will get the primaris power for free. This is called 'psychic focus' so a psyker with a mastery level of one, now gets two powers! Powers outside of disciplines, such as 'force' do not count towards psychic focus....
Generating your powers is done in the same way as before, except there is an additional note, if you have the psychic cards to hand you can just randomly pick your card rather than rolling dice! Now for the new stuff, at the start of each psychic phase, the player who's turn it is rolls a D6, and both players get that amount of warp charges, plus a charge for each mastery level on the table at the time (even in vehicles). Both players adds these up and that becomes their warp charge pools. Once the player who's turn it is has zero warp charges left, the psychic phase ends and all warp charges are lost. The shooting phase would then begin.
Only the player who's turn it is can manifest a psychic power and no unit can attempt to manifest the same power twice in one phase, you are able to go back and forth between psykers and generate the powers at will, assuming you have warp charge left. To manifest a power you need to pass a psychic test. You will need to roll a 4+ for each warp charge needed to manifest a power, and you can elect to use as many dice from your pool as you wish to try and pass the test. If two or more dice rolled are sixes, then you have to take a perils test. There is a new perils table, where the failed pysker will roll to see his fate. You basically will lose a wound and maybe have something else happen to you, like losing one of your other powers.
Deny the witch is still there. Once again you use your warp charge pool to deny the witch, having to nullify all of the successful warp charges to stop the power. There is a little modifier chart for depending on wether you are a psyker yourself etc. but generally you will have to nullify on sixes. Regarding the chart, if you had a psyker in the target unit you nullify on rolls of a five. If your units psyker has a mastery level higher than your enemies you nullify on fours, and there is another +1 if you have the adamantium special rule! You are now able to nullify powers that were not directed at you, such as blessings, but this is only done on sixes, with no modification chart. Once your pool is empty you can no longer deny the witch!
Having a psychic hood with 12" of that unit lets the psyker with the hood take the deny the witch roll
Then there is the usual psychic disciplines, with a new Daemonology type. The new discipline cannot be used by Tyranids. Daemonology is split up into two sets of powers, Sanctic and Malefic with a couple of special rules to go with them. Grey Knights cannot take Malefic, and Daemons cannot use Santic powers. All other psykers that use these disciplines suffer perils on any doubles thrown!
That's it, next up, the shooting phase...