After we have finished meditating, how do we go about contemplating?
Contemplation comes after many years, when one is very advanced in the spiritual life. Contemplation is the highest rung of the inner ladder. Very, very few spiritual aspirants have the capacity to do even limited contemplation, and they certainly cannot do so at their sweet will.
Contemplation must be mastered before God-realisation, so it cannot be ignored or avoided. But, in your case, the necessity for contemplation has not come because your concentration and your meditation are not yet perfect. When your concentration is perfect and your meditation is perfect, at that time your contemplation will also have to be perfected. Then you will really be able to enter into the Highest.