First up the simple answer is you won't. Polyhedral dice are a complex shape made in factory conditions and will never be truly random. Further even if the dice were completely random over time they would wear slightly and the randomness would be impacted.
That said there are a few things you can look for:
Consistent Shape - Any dice should have faces that are exactly the same shape. Any deviation from this will cause problems.
Uniform Density/No inclusions - Anything inside the die that changes the weight distribution will make it less random. Although they are often very pretty fancy glitter and other inclusions are not great when it comes to randomness. One trick if you are trying to get really random dice is to avoid opaque designs. This lets you see if there are bubbles or other inclusions present in the die. You will notice all dice used in a casino are transparent for this reason.
Sharp edges - This one is a little controversial as many sharp edge dice are actually horribly constructed and not nearly as random as they claim. In general the edges of the dice should be crisp and not overly round.
Flat faces - It goes without saying that the faces of the die should be flat and the indentations for the numbers or pips should be shallow to not change the weight distribution too much. Some very high end manufactures actually change the size of the numbers to try and keep the balance perfect. This seems like overkill to use however.
Wear - For the same reason that casinos rotate out their dice periodically you may want to as well. Obviously your dice will last for years of regular play but those dice you got in the 1980s are probably so worn as to be seriously unrandom at this point.
Hope this gives you some more info on what we look for in dice. If you want to buy some new ones check out our store.