Try to last as long as you can without staying idle.
When you use a skill it gains experience, the two bars in the skill background. After it fills up, when a Cycle ends it will gain levels, increasing the progress multiplier for this skill. Bloodline levels are permanent while Generation levels reset when the next generation starts. The table in the end-of-generation recap shows how many Bloodline levels you have earned as well as how many Cycles you spent using each skill. Try spending as many cycles on one skill to level it up faster.