Give UNOOSA the authority to regulate all space broadcasts.
This is a global effort, and someone's going to have to coordinate it and get everyone to comply. Who's it going to be?
As discussed in another answer, there is already UNOOSA, the UN Office for Outer Space Affairs. They, with the help of SETI and national space agencies, are likely to be the ones to coordinate contact with another civilization. They'd be the natural choice to govern the global effort to darken the Earth.
Don't change the speed of light.
The nearest star is four light years away so it will take our signals four years to get there. Then they have to decide to mount a response and fly all the way here at sublight...
Either they're already on their way, in which case we're screwed in 10-1000 years, or they're really far away, in which case we have even more time.
Stay close to the Sun.
If the Earth were a night light, the Sun would be the giant spotlight right next to it. The Sun is so bright and so electromagnetically noisy that it blots out everything the Earth might transmit. The aliens are blinded.
Unfortunately for us, we're getting really good at detecting exoplanets. We're finding more and more sensitive ways to tease information about a planet out of the noise of its star like the composition of our atmosphere and wavelengths of energy we're reflecting (or transmitting).
Being so close to the Sun helps, but we do have to mind what we transmit and how we alter our atmosphere.
Don't fire focused beams into space, only omni-directional.
Take advantage of the inverse square law, when you double the distance of an omni-directional transmission its power drops four times. By the time something like a radio or TV transmission gets 5 light years out, it's very weak; @Green goes into detail. So long as you stick to omni-directional transmissions, you're probably fine.
If you focus those beams, the effect is greatly lessened. Now who would do that?
Shut down all Active SETI projects!
Seriously guys, stop broadcasting focused beams of energy at other stars! It's like shining a laser pointer at the neighbor's window, the space aliens are going to be really annoyed. And stop sending out star maps!
Unfortunately one message has already arrived at Altair 16 light years away in 1999. A map to our solar system, chemistry, DNA, characteristics... let's hope nobody in Altair was listening.
The next three are set to arrive in the 2020s with another five in the 21st century. They sent out everything from the recipe for photosynthesis, to a bunch of text messages, to a full on navigation beacon. Fortunately these are all directed at specific stars, let's hope we get lucky.
Stop sending probes outside the solar system.
These will probably not be picked up as they're very dark and will eventually be very cold and indistinguishable from the background, but just stop it.
Fortunately there's only five already on the way out, and if we really wanted to we could catch up to them with a rocket and strap an ion engine on it (and the rocket we sent) to put them into a solar parking orbit.
We wouldn't want one of them to fall into a wormhole, be given sentience by an advanced mechanical race, and return to Earth in search of its creator, wrecking havoc in its giant nebula ship when it finds us meatbags made it.
Encrypt all transmissions.
Already covered by @Green, if done correctly encrypted transmissions are indistinguishable from random noise. As correctly pointed out in the comments on that question, the communication protocol itself would still be identifiable; however encrypting the data portion would greatly reduce the signal's detectability as being artificial.
Startalk recently featured Neil Degrasse Tyson and Edward Snowden discussing this very possibility.
Stop radiating on unnatural wavelengths.
Even if you encrypt everything perfectly there's still the problem of spewing out all that radiation on wavelengths which don't occur naturally. We use these frequencies exactly because A) they're not common in nature and B) they're not absorbed by our atmosphere. If aliens see a constant stream of UHF transmissions coming from our planet, they're going to know something is up.
The Earth will have to practice some steganography and hide their signals in plain sight. One way to do this is to use wavelengths already common in the universe. Another is to avoid regular patterns of transmission times.
Return the atmosphere to its pre-industrial state.
We can already take educated guesses at the composition of an exoplanet's atmosphere and we're already looking for signs of life or industry in its composition. There's nothing we can do about showing signs of life, the greatly elevated levels of oxygen are a dead giveaway, but we can do something about all the other dead giveaways we've been pouring into the atmosphere.
Stop dumping heat into the atmosphere.
An industrial civilization generates a lot of waste heat which can be detected as unaccounted for extra infrared radiation. There was recently a SETI survey which did this for entire galaxies searching for Type III civilizations (lucky for us, they found no evidence).
Earth people would have to end the practice of dumping waste heat into the atmosphere. It would either have to be sequestered underground or reused.
Send a transmission about that Hitler guy.
One of the first major TV transmissions was the 1936 Summer Olympics in Berlin featuring speeches by Hitler. It's going to be one of the first video transmissions aliens might pick up. Just to make sure aliens don't get the wrong idea, we should send out a final transmission saying "don't listen to that Hitler guy, he's a ****".