Sometimes I get some "dry" clementines with barely any juice, and sometimes they are juicy but bitter. How do I make sure they're juicy and not bitter?
Bitterness can come from underripe fruit (although a lot of times they'll just be sour or less flavorful), lack of juice is usually something that has been stored too long and dried out.
A ripe mandarin or clementine should be firm but not hard with a good, bright citrusy fragrance. Rubbing your finger on the skin should impart some citrus oil (unless it's waxed of coated...) I think usually the smell is the best guideline for flavor, although I have still sometimes had a fruit that smells great and tastes pretty bland. But I think usually if they are really fragrant that's a good sign.
The skin should be somewhat loose-feeling. If the skin is tight on the fruit, it is either not ripe or it is drying out (or it's not a mandarin or clementine).
Don't squeeze the fruit and bruise it, but when you pick it up, there should be a bit of give in the skin. Mandarins and clementines have very thin skins, but these still have the sort of spongy texture of other citrus. Because they are thin, they dry out quickly. It's hard to describe what drying citrus skin feels like - progressively rougher and harder than fresh, eventually turning into a crisp and brittle almost stony layer. I'm sure you would notice far before it gets to that stage, but it's not going to happen overnight. (But the fruit shouldn't be squishy or have soft spots, that is generally spoilage or damage.)
It should not feel dry and hard. A juicy citrus will feel heavy for its size, although for really small ones that's kind of hard to judge.
One more thing to note, though, is that most of the time, the whole batch of whatever type of fruit at the grocery store or at a particular market stall at any given time will very likely come from the same source. While there might be some better and some worse ones, overall they'll probably be pretty similar, unless you can clearly see that some are older or from a different source.
If you're not sure about a batch, just buy a couple and then get more after you see that they're good. (And if you find some great ones, buy a lot and freeze some for juice for later.)
The most reliable indicator of whether citrus fruits are sweet/bitter is their smell. Ripe citrus fruits have a distinct sweet odor mixed in with the citrus flavor.
Hold the fruit some distance away and get a feel for the flavor. The rind of citrus fruits is almost always bitter, so if you hold the fruit too close, all you would smell is the bitterness.
Another aspect is the skin of the fruit. It should be moist and somewhat yielding. Note that clementines bruise very easily because of their thin skins, so be sure not to press too hard. If the fruit feels hard or stretched, it has probably dried out.
Also, most of the weight of a citrus fruit comes from water, so a dried out fruit will feel much lighter than a good one. Dried fruits also tend to "rattle" a bit when you move them around, so make sure that there are no hollows or depressions under the skin.
And of course, there's always the color :). Green citrus is almost always bitter. Try to pick one that is yellow, orange or the like (depending on the type). Dried fruits also tend to go yellow though, so keep an eye out for that.
Note that they are two different fruits. A good mandarine is juicy, but not especially sweet. A good clementine is sweet, but drier than a mandarine.
There certainly are bad mandarines, which are dry in addition to being unsweet (I find them more sour than bitter), and bad clementines, which are not really sweet in addition to not being especially juicy. There are good specimens of each fruit, of course, and it is worth trying to find them. But they are good within the range typical for their fruit type. If this is what you were interested in, see the other answers here, they're pretty good.
But if you think of all mandarines and clementines you've ever had, let's call them "maclems", and insist on finding a fruit which is as sweet as the sweetest maclem, and as juicy as the juiciest maclem, this fruit does not exist.