Double Mission:
There are NO 'kill point' missions or 'objective' missions.
EVERY mission is a 5 kill point mission. EVERY mission is a 5 objective mission.
You need to score MORE kill points AND secure MORE objectives than the other guy in order to get a win.

Kill Points:
Before deployment you and your opponent each choose 5 kill points from his army to be his kill points and vice versa. This is where giving your opponent a spare list comes in handy. Just write it down. You can if you wish still give bonus points for kill points, but I think having bonus points for other things is a better way to go. I'll get into that later.

Objectives:
Every game will always have 5 objectives. In general, one in each quarter and one in the table center. Now comes the part about contest and control that always confuses people, so...time to explain in depth.
Scoring units (meaning Troops that count as scoring in your rulebook) count as two for the purposes of capture.
Non-scoring units (meaning everything else) count as one for the purposes of contesting a capture or providing an assist to one.
Whoever has the highest total points worth of units around an objective will claim it.