Members of the team should come ready to to the planning session with a list of things they are going to be working on. Each task should be scored with story points, an estimate for how long the task is going to take in hours usually using multiples of 8. The scrum master and product manager will put cards that represent tasks on the story board to fill up the length of the sprint for each person.
There are a few deadly sins of planning:
Never do design during the planning meeting. If some members of the team start trying to do design, make the designing as a task with story points.
Never use Fibonacci sequences or shirt sizes for story points. There are people that use Fibonacci sequences for the story points and this should NEVER be done. It makes it difficult to determine how long tasks will actually take.
If planning takes too long, make it an "improve" to talk about at the next retrospective. Time is money.