Stealth

In a age where many radio based systems have fallen into disuse due to effective countermeasures, the Elite Dangerous stealth system is based almost entirely on heat. The range at which you are picked up by a ships scanner is directly proportional to the amount of heat you are generating. If your ship is giving off no heat, another ship has to get very close indeed to properly register you.

There are two ways in elite dangerous to give off little or know heat:

Silent Running

Silent running can be toggled in your ships interface (left panel: functions) or by pressing a key binding. When in silent running mode your shields and radiators will shut down. This means that any heat built up in your ship will stay in your ship and you will be almost invisible to other ship's scanners.

On the downside if you let the heat build up to much your ship will overheat and take damage. You should avoid using excessive thrust and energy weapons (except stealth lasers) while in this state and you should have heat sinks on hand.

Be warned, if you end silent running with high heat you will suddenly show up on all local scanners with your shields still down, make sure you are ready.

Cool Running

Cool Running is when you turn of many ship systems so your ships temperature drops to zero or at least single digits. There is currently no easy way to toggle Cool Running without third party software, instead you must go into the Modules tab of the left ship interface and manually turn off the systems you don't currently need. Cool Running is almost as good as Silent Running stealth wise but doesn't have the time limit imposed by not getting rid of heat.

The systems that you will wish to turn off depend on your situation, if your looking to smuggle illegal goods into a starport for example, you will want to turn of almost everything except drives and scanner. But if you intend to ambush someone you may want to turn off everything but shields and life support instead so when you spring the trap your shields will be fully charged.

Remember you will need to wait until your temperature drops to almost zero and ice forms on the cockpit, alternatively a heat sink can be used to bypass the wait.

Both

The best sneaks and smugglers use a combination of Cool and Silent Running. They will use Cool Running on approach to get their temperature to zero and stay of the scanner, and then use Silent Running when they get up close. The combination of a low temperature starting point and already having many systems off means that Silent Running can last a very long time this way.

And finely it's worth noting that many players turn flight assist off while Cool Running so they can be moving while their drives are off. While this helps it is not in any way necessary in most situations unless you want to approach with your shields ready to go.