Since API Level 21 (Lollipop) Android provides a PdfRenderer class:

// create a new renderer
 PdfRenderer renderer = new PdfRenderer(getSeekableFileDescriptor());

 // let us just render all pages
 final int pageCount = renderer.getPageCount();
 for (int i = 0; i < pageCount; i++) {
     Page page = renderer.openPage(i);

     // say we render for showing on the screen
     page.render(mBitmap, null, null, Page.RENDER_MODE_FOR_DISPLAY);

     // do stuff with the bitmap

     // close the page
     page.close();
 }

 // close the renderer
 renderer.close();

For more information see the sample app.

For older APIs I recommend Android PdfViewer library, it is very fast and easy to use, licensed under Apache License 2.0:

pdfView.fromAsset(String)
  .pages(0, 2, 1, 3, 3, 3) // all pages are displayed by default
  .enableSwipe(true)
  .swipeHorizontal(false)
  .enableDoubletap(true)
  .defaultPage(0)
  .onDraw(onDrawListener)
  .onLoad(onLoadCompleteListener)
  .onPageChange(onPageChangeListener)
  .onPageScroll(onPageScrollListener)
  .onError(onErrorListener)
  .enableAnnotationRendering(false)
  .password(null)
  .scrollHandle(null)
  .load();