Keep it Simple in the Early Going

I landed this decent mirror today using
sweet corn on the hair rig (at right).

The simple approach is the best approach in the early season for carp.  Sweet corn, whether you put it directly on the hook or on the hair rig, is your best bait. A 50 cent can of corn from Walmart might last you a few outings.  It's best to chum with it a bit before fishing. In addition, keep the leaders short and use small sinkers that are big enough to hold bottom. Method mix can be used or you can go without it.
A key early success is to find fish that are willing to hit. At this time of year, the carp tend to be bunched up.  Find one and you tend to find many. As a rule, shallow ponds that warm quickly tend to fish better than deeper ponds.
I have been having decent success in the last couple of days while using a simple approach.  Things will get more complicated as the weather warms in May, but for right now, keep it simple.