Gas turbine internal wash? Depends entirely on the engine and installation, and whether the wash is for desalination or pressure recovery. Desalination; H20 only, make sure its clean. Power recovery, solution of a commercial chemical, such as Zok, always followed by fresh water rinse. Might need to be heated, depends.
Engine manufacturer will specify engine preparation, which might include blanking/disconnecting things like FCU sensing lines and removing igniter plugs, and de-preparation which might include draining some parts of the gas-path. Always followed by a drying/check ground run. Airframe manufacturer may specify blanking/disconnection of bleed-air feeds.
Prodedure and tools? Depends. Sometimes the engine installation includes compressor-wash plumbing with a quick disconnnect on the cowling, others may have a hand held spray lance. More often than not, supply is from a large pressurised set of tanks on wheels, such as from Tronair. At its simplest/smallest, an adapted fire extinguisher. Don't do it if the engine is too hot, or atmosphere too cold. Establish communication between cockpit and wash-guy; work out who is doing what, when, and for how long, and an "It's all gone to sh1te" signal.
Runoff? For water only; anywhere the real-estate holder doesn't mind the mess. Chemical; lets quote the good-old "local regulations".
Precautions? Its a rotating engine, act accordingly. Remember it may (or may not) have a propeller attached, which may (or may not) display varying levels of enthusiasm to rotate. Hazard data sheet for any chemical.
Try not to get wet.