I anticipate that we will not detect radio emissions from other civilizations due to the inverse square law of radiation. The best chance for us to detect alien life will be to image it directly.

The galaxy is 100,000 ly (9.4605284e+15 meters) across, so we will want a telescope that can see 1-meter-sized objects on the surfaces of planets at that distance. That's an angular resolution of 6.0562980e-20 degrees. Of course I'm being ludicrously optimistic. But what the hell. I'm not an astronomer, so who cares.

According to various sources the formula for the resolution of a telescope is:

sin(theta) = 1.220 x lambda / D

where,
theta = angular resolution
lambda = wavelength of detected radiation
D = circular diameter of telescope aperture or array size

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If we want to see a planet with green vegitation during daytime we would use a visible wavelength (~550 nm). D = 634,801,455,640,000 meters (4243 AU or 54 x diameter of Plutos orbit)

If we want to see a planet with warm bodies even at night we'd probably choose an infrared wavelength (~10000 nm). D = 11,541,844,705,455,450 meters (77152 AU or 977 x diameter of Plutos orbit)

note: 1 ly = 63239 AU

If we had a REALLY fast spacecraft we might be able to deploy such an instrument. Coordinating their pointing direction and distance would again be a supreme challenge. Might be just the thing for us apes to try. I bet the Air Force could do it. We would need something about 50x faster than the Voyager probes to deploy to those distances within 5 years.

I have to say that I would really think this is a challenge worthy of NASA. Forget Mars. Its dead. Lets build a telescope that can image the whole damn galaxy.