Inside the space, you will see filters for ALL, FAVORITES, MY TASKS, ACTIVE, and COMPLETED. Choose the MY TASKS link to see only tasks that have been assigned to you.
TIP: In your Home page, you can change the settings of tasks you are assigned to so that you are listed as a Follower instead of an Assignee. This will remove the task from your Home page but still allow you to receive notifications about the task and view it in the space. Click here to read a knowledge base article about setting yourself up as a task follower: http://support.kona.com/entries/22074323-what-does-it-mean-to-follow-or-un-follow-a-task.