Great that you enjoy that little luxury in your mornings! Making that fresh coffee and enjoying it while waking up can be such an awesome mood booster.
As already answered: Knock the portafilter against the edge/wall of your bin and the "cake" should just fall out. There are also special little containers with a little (afaik often rubberized) bar on top for exactly this.
Then just rinse the basket and done :)
Get yourself a nice little (fine tuned) scale for measuring the beans and a grinder (e.g. the Porlex Mini is affordable, very good and holds enough beans for a double shot espresso) and get down to experimenting to get your perfect coffee.