Especially like the sandy Sahara. I read a little and found said desert lost its lushness from a change in Earth's tilt. Are there other reasons?
It is correct that equatorial areas typically are hotter due to greater exposure to the sun. However, that doesn't directly impact rainfall. There are very wet areas at the same latitude as the Sahara, like Thailand and central/south America.
There are other factors, like forestation, but the simplest overview is to say deserts are based on air currents. Rainfall is determined by how moist the air over a region is. Air over oceans, especially hot air, becomes saturated with water. When this air blows over land masses, it results in rain. Typically, mountains are involved as well, as mountains can block cloud movement and create temperature differences which prevent moisture from moving beyond them.
If you look at a chart of wind currents, like this one, you'll notice that deserts lack moist air currents (those that have been over oceans recently), and that jungles typically have direct winds blowing on them from the coast. This is why it is possible to have deserts directly on coastlines: if the wind moves away from the land, it has no impact on moisture.
It is also worth pointing out the direction the air currents move in depends on which side of the equator you are on. On a normal map, above the equator they move clockwise, and below counter-clockwise. This is heavily impacted by land masses, but is a general rule. Such is caused by the planet's rotation. Not every point on the Earth's surface rotates with the same angular velocity. Effectively, equatorial areas move faster and polar areas slower.
One of the best articles I've found on this topic can be read here. From the article:
The location of deserts is dependent on two factors, latitude and global wind patterns.
Latitude has an impact because of the temperature gradient across the Earth. Most deserts lie between 15' and 35' latitude. Looking at a map of rainforests will reveal that most rainforests also lie between these latitudes. Rainforests (and mountains) are what create deserts. Warm, damp air rises off oceans, carrying lots of moisture. This moisture is deposited in the rainforests, until the air has no more left. At this point, the air is very dry. The next region it passes over (until it passes over ocean again) will be a desert, receiving very little rainfall.
Wind patterns are important because they are what make the damp air move. Most deserts are between the Northeastern and Southeastern trade winds belts. These two air currents carry the air over land, where it loses moisture, then creating a desert further on.
Generally, a desert is defined as an area that receives less than 10 inches, or 25 centimeters, of precipitation a year.
Emphasis mine. Precipitation is emphasised because it can come in the form of either rain or snow. Deserts that mainly get rain are hot deserts, deserts that mainly receive snow are cold deserts.
Another defining factor for a desert is temperature swings. Because the air in a desert is so dry, there is nothing to hang onto the heat it receives in the day, so the temperature drop is quite large.
In the Köppen climate classification, there are 3 different kind of deserts:
Hot desert, Cold desert and the Polar climate. The last one is not always a desert regarding precipitations but it is too cold for the vegetation, so I'll include it in the deserts. A desert can receive some rain and can even have some vegetation. A desert is classified as a place where the evaporation rate is much greater than the precipitations. Hot places require more rain to keep them from turning into a desert. Near the equator, almost 2 m of annual precipitations are required to keep the climate classified as wet. While other places like Siberia would require possibly less than 100 mm of annual precipitation.
To figure out where the deserts are, it is important to understand the wind circulation. It is rainy where the air pressure is low and dry where the air pressure is high. Low pressure areas are drawing the surrounding air masses toward them with all the humidity it contains. But the high pressure zones are drawing the air form the higher part of the atmosphere. This air is not always cold but it is dry. Theoretically, the two places that are mostly high pressure are the subtropical ridges (near 30 degrees of latitudes) and at the poles. This is why the Sahara and the Antarctica are desert despite being surrounded by the sea at some places like Saudi Arabia. This is where you will find the hot desert and the polar climate near the poles.
Of course the landmasses will influence on the pressure. Large continent become hotter in the summer and create larger low pressure zones. On the opposite, Siberia is very cold in winter and thus creates a very high pressure area. In the Northern hemisphere , the high pressure area is not over the pole but over eastern Siberia.
That is also why India is not a big desert. Since Asia become very hot is drive precipitation toward the land.
Some places are deserts even if the air pressure is low and we should expect some precipitations. It usually happen when the rain is blocked by the mountains like in Lima, Peru.
Deserts that are located at higher altitudes or at latitudes over 35-40 are mostly cold deserts. The most important characteristic of these deserts is that they are always located deep inland or near mountains that are blocking the winds. They are much drier than the hot deserts as they barely receive any rain. Normally at these latitudes, the quantity of precipitation require to have a wet climate is not that high. You don't find a lot of deserts near the sea for example. If it is near the sea, the winds are blocked by mountains.