Fishing with pop ups is a very effective method for catching Carp and some very big Carp at that!
It is essential you use the right rig to get the best presentation and reaction to a bite. Some rigs are dedicated to using pop ups and wafters, some are suitable for all bait types and some are just for bottom baits. So what Carp rig do you choose and why?

Ronnie/ Spinner rig

Ronnie rig like Tom Dove uses.

The most popular rig for pop ups at the moment has to be the Ronnie Rig or Spinner rig. This is essentially a rig which allows you to present a pop up just an inch or so off the bottom. The rig itself comprises of a stiff boom section (although a coated braid can be used) and then the hook is mounted on a specialist ronnie or spinner swivel. This rig is what is favoured by Tom Dove, Neil Spooner etc. and can come under many different names such as "the Ronnie boys" (OMC) The Spinner Rig (Korda) (they remove the large ring from the Ronnie swivel) The Rotator (Ridgemonkey) All of these are the same rig just the marketing is different.
The ideal presentation is for the boom to lay flat and then the hook to fall slowly through the water, this will ensure your rig is sitting on top of any leaves or debris that may be on the bottom. The hook should sit up right like a claw. With this rig you should test it prior to actually casting out and fishing.
The stiff boom material will help to prevent any tangles that may occur during the cast and should you have an aborted take the rig will simply reset itself ready for the next bite.
With the Ronnie or Spinner rig the bait is mounted on the shank of the hook via a bait screw, micro flexi swivel or a rig ring.
This rig has had many adaptions in recent years from adding a hair to the shank to allow you to hair rig a bait, to combining the Fluorocarbon D rig style of presentation, this is acheived by creating a D section using a fluorocarbon.
Ronnie or spinner rigs can also be used very effectively in a PVA solid bag however, the rig should be made with a supple braid such as Fox Reflex, Korda Dark Matter (Uncoated) or Korda Super Natural.

The Chod and Stiff Hinge Rig

This is one of the classics, they are practically the same rig. The chod rig is a very short rig normally only a inch or so long and has a Flexi swivel on the end. This allows you to slide the chod rig on to your leader if you use them or your mainline if you are fishing the Naked Chod rig. This rig is perfect for when there is leaves and decaying weed on the bottom of the lake. The trick to using the Chod rig effectively is to get your chod beads in the right position, you dont want the bottom bead to near to the lead as this may cause the rig to bury itself in the debris, instead, you want it about 2 or 3 inches above the lead sometimes even more than that. The top chod bead can be set at what ever distance you would like however, if a fish picks up the bait and moves towards the rod you may not get an indication of a bite if the top bead is too far away. I find about 2 to 4 inches seems to work best for me on the waters I fish. Like all the other rigs you may find you need to add some rig putty to this rig to get the perfect presentation. The rig putty should be molded around the bottom crimp. When you test this rig you want the rig to sit upright and the swivel to touch the bottom.
The stiff hinge rig is the same rig except it has a stiff boom added to allow you to fish this rig on a lead clip or even better is the helicopter style.