There's no easy, at-home way to tell. Some scales are supposed to be able to tell if you use them barefoot, but from everything I've read, the at-home models are not extremely valid or reliable.
And for most of us it just doesn't matter, because water AND fat add to the weight we don't want to see in the mirror. What we don't want to lose is muscle (because the muscle lost from too-low protein/calorie diets can come from anywhere, even the heart).
The biggest test is how your food plan works for you most of the time (and if it's a new food plan, give it a few weeks before you decide).
If you lose weight most of the time and suddenly see a gain, even though you haven't changed your food plan - the the weight gain is probably water, especially if it's PMS/TOM or you've increased your activity level or if you're not feeling well - the body needs extra water for all of these events. Give it a week. If you're still gaining, then your food plan may be too high calorie or too high carb for you, adjust and repeat from the beginning.
Likewise if you're within your calorie budget, but you're eating more carbs than your normal, it's probably weater gain. If you're eating fewer carbs than your normal and you see a loss, but your calories are about the same - the loss is probably mostly water.
... the test of water loss are mostly time-related. Only in hindsight do you start to see patterns, but they do help you in the future make an educated guess (though time will tell).
I know certain foods and activities cause water gain and loss, but I can't guarantee how much of a gain or loss is exactly from the water, especially if I'm not behaving consistently enough to know.
If I eat a restaurant meal, I know I will gain water. If I had a good idea of the caloric and carb content of the meal, and I stayed within my budget, I can be fairly confident that any gain will be water that will be gone in about two to three days (if it's TOM a week) if I stick to behaviors and foods that don't aggravate water gain (or don't promote fat gain).
However, if I overate and don't know approximately how many calories were in that meal, I can't tell how much of the gain I see will be water, and how much will be fat.
Either way, a few days will tell me whether the gain was temporary or not.
If all of the extra weight is off two days later, that pretty much tells me that it ALL was water weight. If it's not, I can't be sure.
I can tell if I'm retaining water heavily by the shape of my face my wrists (and if a thumb print into the skin leaves a white print that doesn't disappear virtually immediately).
But ultimately if you can just focus on your food plan, it doesn't matter at all, because your food plan will eventually deal with both kinds of weight gains. If you don't worry about why you're up a pound, it doesn't matter why, because staying on plan with deal with both types of weight.
When you switch to a higher carb plan, from a lower one you have to be ready for that weight "gain" though and not let the gain convince you that you're doomed to gain all the weight back if you eat one carby meal. Yes, you'll gain some water (because the body needs more water to digest carbs) but it isn't necessarily fat. The only way to tell if it's fat, is to keep on the new food plan. If the gaining doesn't stop after a week, there's a good chance you're dealing with fat gain, not water gain and you'll have to adjust your calorie level to start losing again.
We make the numbers much more important than they have to be. How you're eating, and how you're feeling is the most imporatinant thing. How you're looking in the mirror can help too (especially when you're close to goal, but even when you're 150 lbs away from goal like me, you can often tell the signs of water bloat in your face, wrists, and ankles).
Experience will help ease your mind, but so will trusting in your food plan.