Yes! And It's Really Easy!
You're in luck! Many, many, many easy chemical reactions result in water. This is why sci-fi shows depicting people with powerful starships fighting over water is kinda silly, it's 19th century chemistry.
Some of them are exothermic (they generate heat and thus power), and some are endothermic (they require power). Depending on what materials you have, making water can either take power, or be a byproduct of generating power. So long as you have power and a source of hydrogen and oxygen, you can make water.
One side of the planet is always in sunlight giving you a VERY reliable source of solar power. And there's no atmosphere to block the Sun. The main problem will be heat dissipation, that can be solved by putting them near the day/night terminator. They can even be on the night side for cooling, but placed high up to peek over the horizon.
Another source of power is heat differential. Since the planet is tidally locked to its star, and there's no atmosphere, the two sides will have enormous temperature differences. This can be used to generate power. A simple thermocouple spanning across the day-night terminator will generate power. Similarly a heat engine spanning the terminator can generate power.
Once of the simplest means of getting power would be to set up a solar thermal collector. It doesn't require much in the way of fancy materials. Set up a tower of salt, or other material with a high specific heat and a high melting temperature, just on the night side. The tower is high enough to peek above the horizon. On the day side, set up solar reflectors to concentrate sunlight onto the tower. This heats the salt which can now be used as an energy source. The extreme temperature difference between the molten salt and the frigid night side makes it all very efficient, and vacuum makes a great insulator. An example of such a thing today is the Ivanpah Solar Power Facility.
Oxygen, Oxygen everywhere, but not a drop to drink.
Water is 2 hydrogens and an oxygen. If you have hydrogen and oxygen gas, they react to make water... quite explosively. If you run a current through water, you get hydrogen and oxygen.
Hydrogen is extremely abundant in the universe, it is the most abundant element. Oxygen is also very abundant in the universe, great! Great news for our crew! Odds are they'll find lots of compounds with lots of hydrogen and oxygen on their planet.
Oxygen loves to react with things to make stable compounds, this is not so good for our crew. Oxygen loves to strip electrons and hang onto them, oxidizing, making oxygen compounds very, very stable and releasing a lot of energy. Burning is oxidation.
It's not enough to just fine compounds rich in oxygen and hydrogen, they need to find compounds that can be coaxed into reacting to form water. And once oxygen has made a compound, it does not like to let go.
For example, as others have pointed out, "desert planet" implies sand which is mostly Silicon Dioxide. The problem is it's very stable and does not like to react with other chemicals. Sand doesn't burn because burning is oxidation and sand is already oxidized.
But fluorine loves electrons even more! If you have a source of Hydrogen fluoride around, it will react with Silicon Dioxide to form Hexafluorosilicic Acid and Water.
SiO2 + 6 HF → H2SiF6 + 2 H2O + Heat
Since fluorine is involved, this will probably be a very energetic reaction producing heat which can be used for power.
Another reaction is to use a strong base like Sodium hydroxide, plus heat, to produce water.
SiO2 + 2 NaOH + Heat → Na2SiO3 + H2O
Those are just two simple examples. There's any number of ways to produce water with different compounds and amounts of power. There's so many there isn't much point in listing them all, hydrogen and oxygen are so abundant, and their race is advanced enough to have interplanetary space flight, the folks on your planet will find something that works. At the worst they can recycle their own waste.
The next problem is purification. Water isn't much use to people if it contains Hexafluorosilicic Acid.
Fortunately, with enough power, water purification is easy: distill it. For our example of a solution of Hexafluorosilicic Acid, it decomposes at 108C just above the boiling point of water. Boil the solution and condense the vapor in a new vessel. You're left with a jar of clean water and a concentrated solution of Hexafluorosilicic acid.
Come to think of it, you don't even need the power. The boiling point of water depends on its pressure. Drop the pressure and the boiling point also drops. Since there's no atmosphere, it's trivial to make a vacuum still. This takes less power, and the lower temperature avoids denaturing the dissolved compounds.
In chemistry there is no "waste", only byproducts waiting to be used in another reaction. In the case of our concentrated solution of Hexafluorosilicic acid, we can react that with another chemical to get more water. Say, aluminum oxide, also very abundant.
H2SiF6 + Al2O3 → 2 AlF3 + SiO2 + H2O
That leaves us Aluminum Trifloride and Silicon Dioxide. We can use the Silicon Dioxide with more Hydrogenfloride to make more water. And the Aluminum Trifloride can probably be reacted with something else and so on and so on.
So long as you have energy and material you can keep these reaction chains going indefinitely, extracting hydrogen and oxygen in the form of water.
Offworld Ice Mining
It turns out there is a lot of water floating around out there, the universe isn't nearly as dry as we thought. Your crew could literally mine water off asteroids.
Since the planet has no atmosphere, there's no pesky drag to worry about, and its much easier to get off planet. You need far, far less power, and there's no heating issues to worry about.
Conventional rockets need huge boosters to get through the atmosphere. They go straight up to punch through the thick lower atmosphere as quickly as possible, then turn sideways to increase their orbital velocity. This is inefficient, all that power spent going straight up could instead be used to get to orbital velocity. But it turns out it's more efficient to get high up and decrease your drag first.
With no atmosphere there's no drag. No drag means less power is required. No drag means the rocket can follow the most efficient trajectory to orbit, which also means less power. Less power means smaller engines and less fuel. Small engines and less fuel means even smaller engines and even less fuel. This is the Tyranny Of The Rocket Equation in reverse.
So your crew will find it much easier to get off their airless planet than they did to get off the Earth. Depending on how damaged their craft is, they could salvage a small spacecraft from it, fly it to a nearby asteroid, move it into orbit around their planet (or just crash it into the planet, it's not like there's an ecosystem to wreck), and mine it for water and other elements.