What I've been doing is first remove the slide and grips. Then, using lots of RemOil (sprayed through the supplied tube) down into the nooks and crannies. I scrub the exterior stuff with an old tooth brush if needed. Then I use compressed air or more RemOil to blow out down and behind in the difficult places.
Since I started lubing the gun with tiny amounts of Mobil-1 synthetic engine oil, the "non-detergent" additives seem to be helping to float most of the crud off and out.
The thought of using a thinner such as brake cleaner, carb cleaner, or other solvents that remove all oil seem to be backwards thinking to me. Yes, you want to remove deposits and crud, but if you also remove all the oil... it's sort of like throwing the baby out with the bath water.