It is actually fairly easy to trap a mosquito resting on a wall or other surface if you use a cup or jar to trap it and pass a sheet of paper underneath so that it doesn't escape. If you put the jar with the mosquito in the freezer for a few hours you will be able to take a good photo without having to immobilize it first (possibly resulting in squashing it). You can also use insecticide, but this should be used with caution and moderation. When taking pictures of adult urban Aedes, it is important to make sure that the white lines on the head and thorax are clearly seen.
Take the mosquito by the legs, focus the camera, and take pictures of the head and thorax. If possible attach 1 or 2 more photos of the abdomen and legs. For breeding sites attach 2 photos: one to help situate the breeding site, and another showing the stagnant water with larvae and/or pupae.