There's two ways to do this. First is to explain why the desert planet has a stable atmosphere suitable for humans. Second is to simply say humans happened to show up at a time in the planet's history when it happens to have an atmosphere stable for humans. Depends on what kind of story you're writing.
If It Didn't, There Would Be No Story
If this is a planet that humans chose to colonize, then it wasn't chosen by chance. It was chosen because it happens to have the right circumstances right now to be suitable for human life. And there's enough planets out there that you're going to find at least one of even unlikely configurations.
The atmosphere doesn't have to be stable. While over geological time it might become unsuitable for humans, that's still time for thousands of years of civilization. And humans have proven very good at altering their atmosphere even accidentally.
So, for the purposes of your story, you can lean on the weak anthropic principle which basically says if the environment were not suitable for human life, we wouldn't be there to complain about it. You don't have to explain why it has a suitable atmosphere, the colonists might not even know, it just does. If it didn't, then they would have chosen some other planet with a suitable atmosphere. Even if they didn't choose the planet, even if they crash landed, if it didn't have a suitable atmosphere there would be no story.
With that bit of hand-waving out of the way, let's go into the issues with keeping an atmosphere suitable for humans.
Atmospheric Oxygen Likes To Party
Contrary to the sci-fi trope, you're more likely to find abundant water than you are to find abundant oxygen. Water is a byproduct of many, many exothermic reactions and relatively stable. If you oxidize (ie. burn) many things, you get water and lose O2.
The problem with a nitrogen-oxygen atmosphere is oxygen likes to react with everything; that's why we call it "oxidizing". If your planet, for whatever reason, developed a nitrogen-oxygen atmosphere suitable for humans it would be difficult to maintain it. Over geological time the oxygen would react with any number of things to produce other substances (such as water) and the atmosphere would become unbreathable.
In order to maintain a level of oxygen comfortable to humans, you need some mechanism that continuously replenishes atmospheric oxygen. Or you need humans to show up at just the right geological time, another application of the weak anthropic principle.
On Earth the mechanism for sustaining the atmospheric mix is life. Life is continuously maintaining the atmosphere's careful balance to sustain itself, while also evolving to match long term changes in the atmosphere. Photosynthetic organisms add oxygen, aerobic life removes it. IF you decide your desert planet has life, it would also have to need a nitrogen-oxygen atmosphere.
Making atmospheric oxygen by geological means is a problem. Because it is SO reactive it requires complex chemistry and energy to make it. This is why, for example, it's a by-product of photosynthesis. Plants get free energy from the Sun, use it to get the carbon they need from CO2, and O2 is the byproduct.
Humans can withstand large variations in the partial pressure of oxygen, but not of other trace gases. Carbon dioxide, for example. At 0.5% it will cause headaches and fatigue. At 1% you get drowsy. At 7% you die. Since carbon dioxide is a byproduct of many chemical processes, you need something removing it from the atmosphere.
On Earth, this is plant life and other photosynthetic organisms. Photosynthetic organisms remove CO2 (they need the carbon), aerobic organisms add it.
There are non-biological ways to remove CO2. For example, quicklime will react with carbon dioxide to form limestone. Large areas of the necessary minerals could be exposed on the surface absorbing CO2. Some mechanism, perhaps wind & grit perhaps geological uplift, would continuously scrub the surface exposing more fresh material to react with the atmosphere.
CO2 is just one problem. You don't want, for example, too much arsenic in the atmosphere. Or even naturally occurring radioactive elements. Accounting for why each and every one of them isn't present at toxic levels gets a little tiresome.
In sum, unless this is a key part of your story, take the well trod sci-fi road and just don't explain it. There's enough planets in the solar system that humanity will find one desert planet at just the right time in its geological history to happen to have a nitrogen-oxygen atmosphere where the levels of toxic gases aren't too high.