I'm trying to get a NavigationDrawer working with sliding tabs inside a fragment (just like google play music or the google i/o app). In all my reasearch I found that you can't use Action bar tabs + Navigation Drawer together because the Navigation drawer will look like in the back of the tabs (I notice that). Can anyone help me telling me how to get that done without use an external library such ActionBarSherlock or TabHost (according to the documentation is recommended the use of actionbar)?
Yes, you're right. It won't be possible using ActionBar tabs as the navigation drawer won't overlap them. I recently implemented a library called ViewPagerAddons which has a custom view called SlidingTabLayoutColors imitating the behavior seen in Google Play/Music.
But as you said you don't want to use any libraries, you can still have a look at the source code. Here's the link with instructions: https://bitbucket.org/enthusiast94/viewpageraddons