Distance Measure

How do they measure distance in light years?
Astronomers tell us that Star X or Galaxy Y is 10 billion light years away. How do they know? They have never been there. They don't have a ruler telling them that the star is that far away. What are they using to help them to tell us about these vast distances?
And how can they measure the Milky Way Galaxy? They tell us it is 100 million light years across. What is the standard they are measuring it with?
Sorry, I never took physics or astronomy, so put it in layman's terms if possible.
Thank you darkphoenix262 for your correction on the size of the Milky Way Galaxy.
All these answers mentioning parallax, but in essence, measuring a star's distance using the Earth's orbit as a baseline is basic trigonometry.
Imagine an iscoceles triangle, where the base is the "diameter" of the Earth's orbit, and the sides are the line from the Earth to star at, say Jan1, and the line to the star at July 1.
It's such a long thin triangle because although the Earth's orbit is 300 million km across, the distance to the star dwarfs it to such an extent that the angle at the top of the triangle (mathematically speaking, the angle that subtends the Earth's orbit at the star), is less than one second of arc for the NEAREST star.
Though the angle is tiny, it can be measured for the nearest stars.
An easy way to work it out is that a radian, which is the angle subtended by the length of a circle's radius projected onto the arc of the circles, is about 57 degrees. Therefore, if the parallax angle to the star is one second of arc, ( a scond is one 3600th of a degree), then the distance to the star is 57 times 3600 times the width of the Earth's orbit.
This distance is termed a Parsec, and is also another measure astronomers use, and is about 3.26 light years. No star is that near, as I said above, the nearest star has a parallax angle of less than one second of arc.
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