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How are scientists able to see and know the activity of outer galaxies? How are scientists able to know how far away stars are? How are scientists able to know what stars are composed of?

Astronomers use telescopes to see things far away - does that answer the first question? There are all kinds of telescopes (visible, radio, infrared, x-ray, space-based, ground-based, mountain-based..., single-lens, single-mirror, multiple-mirror, multi-site interferometers etc.) but they all work kind of the same way: you point it at somewhere in the sky and look at what kind of electromagnetic signals are coming from there. Distance can be determined very directly for nearby stars by a technique called parallax - as the earth goes around the sun the star looks like its moving, and the extent of the motion goes down inversely with distance. For further stars there are a whole sequence of things based on "color" (see next answer) and type of star that seem to follow very standard rules. What stars are made of is determined through "spectroscopy" which is a detailed analysis of the different wavelengths of light coming from the stars. Different elements emit or absorb light at very special wavelengths, and thus leave their "signature" in the light coming from the star.

Arthur Smith

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