The inanimate object that represents Libra in the zodiac is an even scale, not unlike the one found in the hand of a Justice statue. For a scale tattoo, consider just the scale by itself or one measuring two things in your life that have the same value, such as the names of family members or other loved-ones. The design of the scale can be as elaborate and detailed as you want but keep in mind, the more detail in a tattoo, the larger it will need to be.
The signs of the zodiac are often represented by ancient Greek letters. The Greek symbol for Libra is an Omega, just above a horizontal line. An Omega, more or less, looks like an "O" that doesn't connect a the bottom but instead jettisons out on either side. This ancient symbol for Libra is ideal for a small and simple tattoo design for first-timers or people who just don't want a lot of ink on their skin.
The symbols in the zodiac are all derived from star constellations. The one specific to Libra is a 6-star design with four of the stars in an undulating line and two underneath. Consider either stars or simple dots signifying each point of the constellation and whether you would like a small line connecting the points or each standing on its own. This is a design that will require explanation to most who inquire, as it is a more abstract way of representing Libra.
Consider adding certain scripts, such as your last name and the date of your birth to any of the ideas in the other sections to make the symbol a little more unique and personal. For instance, you can design the scales to appear engraved with these letters and numbers or instead of stars in the constellation, consider each point to be the numbers forming the date of your birth, 100483 if you were born Oct. 4th, 1983.