What's the best way to clean my bike?

Either way, the bike will be safe to ride and handle after cleaning, right? One way to tell for sure. Take it past your local bicycle shop for a free inspection. After sitting so long, the brake & shift cables could need to be lubed, or worse...changed if they are rusted up. In any damp or humid environment, anything is possible. The chain will definitely need to be lubed, if not cleaned & lubed. The derailleurs could also need a shot of light chain oil. Who knows? I'm not there to physically look at it. In any event, avoid getting water into any areas that contain bearings. Don't flip the bike over as one suggested. Cleaning a bike up is a long & tedious process. I kinda like the way Old Hippie does it.

Do as Old Hippie says for cleaning, except at this point, after all those years of use and storage, I wouldn't care much about getting watter on the bearings. I think that you should open all the bearings and remove all the old grease and pack new grease anyway. You also need to replace the tires and inner-tubes and also the cables and housings. Check for wear in the sprockets, chain and chain rings and replace as needed.

Forget about the rats turds. Get bike out and turn upside down so it is sitting on saddle and handle bars. Wash the frame down with strong solution of washing up water, rinse down. For the wheels use an old toothbrush between spokes using jif/cif or any cream cleaner. For awkward places I use paint brushes with the water. When finished don't forget to wash down the yard. Don't forget to wash the bits that are upside down.

Use a gently spray from a garden hose to wet it down. Use a bucket with auto wash and a rag to wipe it down and rise it off with a gentle spray from the hose again. Don't stray water directly into the bearings on the wheels, bottom bracket or the steering head.