By no means do I wish to sound patronising at all in this little 'lesson' but, to me, listening to what a girl has to say is one of the most important things a guy can ever do; and trust me it makes a big difference.
Now, coming from experience of actually being a girl myself, I am fully aware that some of the things that spill out of our mouths are complete rubbish and may be of no interest to the opposite sex. Regardless, whether she's telling you about her day, complaining about something/someone, or confiding something private about her life, you should always make the effort to listen and appear somewhat interested in what she has to say.
Saying this, please don't force interest in your voice as this may generally lower her confidence in you and draw her away from feeling like she can talk to you in both simple or important situations. If you genuinely have a interest in her, then you should also be interested in what she has to say.
Learning to tolerate 'dribble' will be hard at times but responding with interest will show that you appreciate her just the way she is. Additionally, her faith and trust in you will grow over time allowing your relationship, whether romantic or friendship, to grow stronger and more stable.
So the next time she comes up with a conversation that you don't necessarily have an interest in, go along with it and don't complain or undermine her. Going along with a conversation, no matter how 'boring', won't kill you. After all, the magical thing about conversation is that something else will come up - something that you might both been interested in - and the boring conversation will be forgotten.