Read out loud as fast as you can!
Ok, maybe not as fast as you possibly can. But, at least at a normal conversation speed, or a little faster if you can do that.
I find that reading out loud, even if I don't understand what the words mean, helps to improve my accent. It also helps prepare you for encountering words you haven't seen before. You have to know or at least guess how the word sounds out loud.
I say fast because it puts more pressure on you to say it right without thinking about it. If you work out the meaning of each word as you go, it'll take forever to read one paragraph.
You also expose yourself to new vocabulary. You may not know the meanings but you will see it in context and it will help you the next time you encounter that word.
It also helps with that little inhibition about public speaking - there's something about hearing your own voice speaking out loud in a foreign language that gets you used to the idea that you can speak a foreign language. I think it helps prepare you for that moment when someone springs it on you in real life for the first time. You already know what your voice and accent sounds like out loud, so it doesn't frighten you.
I think too many people practice their foreign language in their head too much. It can help, but you have got to get it out of your head and into the world.