Let's get this straight: attenuation is a good thing. It is what makes the radar useful in the first place. If you really know what your are looking for, it will help you identify a thunderstorm from hundreds of miles away. And that's good.
What follows are quotes from the sources listed below, as well as my comments in blue.
Figure: Radiated beam reflecting off rain drops, from Honeywell Radar Training, Part 4, Slide 4.
Attenuation is the idea that the radar signal loses some of its strength as it travels through the weather. It serves two vital purposes:
Figure: Radar attenuation shadow technique, from Honeywell Radar Training, Part 4, Slide 7.
You need to aim the tilt down far enough to paint lots of ground clutter and then look for returns. The entire beam has to fall into the weather. More about that: Procedures & Techniques / Radar - Beam Width.
A large return with no shadow is more than likely a city. A large return with a shadow is probably a lake, a tall mountain, or a thunderstorm.
Portions of this page can be found in the book Flight Lessons 1: Basic Flight, Chapter 28.
Honeywell Airborne Weather Radar Training, Rev E, 12/09/02, Honeywell Inc. Commercial Flight Systems Group, Phoenix, AZ.
Honeywell Primus 880 Pilot's Guide, Pub. No. A28-1146-102-03, Revised January 2006, Honeywell International Inc. Commercial Electronic Systems, Glendale, AZ.