Well first of all, the Karma concept is different from the final judgement in western religions. There isn't a creator or omnipotent entity that tallies up your deeds and determine which animal you turn into. Karma simply describes a causal-effect relationship. Your thoughts and habits (cause) tend to sway you do things a certain way (effect) which leads to some outcome (good or bad). That outcome becomes the new cause for the next effect. So Karma describes this continuous chain of cause and effect.
At the time of death, the Karmic forces are still active. A person's thoughts and nature carries on into the next life. During the transition the karmic forces could steer a being to select one life form over another based on their inclinations. So think of Karma as a force of attraction or similarity and not a form of reward/punishment for good/bad deeds.
There's also ancestral karma as well as individual karma.
I think of it like a bank account.
Additionally, accrual of any karma causes reincarnation.