An airship pilot has three ways of adjusting lift:
Every lighter-than-air vehicle needs some ballast to adjust its weight. This could be sand, but mostly water is used.
A blimp is only partially filled with helium. The envelope is held taut by filling a bag inside with air, called a ballonet. If you press a little more air in this bag, the overall density of the gasses in the envelope goes up, while the volume stays practically constant. This allows for fine adjustment. Forward and aft ballonets even allow for trimming the pitch attitude.
When the airship moves, the air does provide a little dynamic lift or downforce, depending on pitch attitude and elevator deflection. This is a little tricky, because airships are not stable, and a pitch-up command will lead to altitude loss below a critical speed.
The ballonets in this cutaway drawing of a Goodyear blimp are numbered 2 and 4.
On a calm day, the biggest disturbance is actually the sun. If the envelope is exposed to direct sunlight, it will heat up and the gas within will be heated as well, causing the blimp to rise. If the sun is covered by a cloud, the gas cools down and loses some lift. On partially cloudy days it is not easy to keep the same altitude!
Another threat is an unstable atmospheric temperature gradient. Glider pilots love this, because it will give them strong thermals, but the gas inside the airship will behave similarly to that bubble of warmer gas which causes thermals. When the airship rises, the gas inside cools less quickly than the surrounding air, and the airship will gain lift when it goes up. It becomes really bad on the way down: Now the gas warms up less quickly as well, and the airship loses lift as it comes down. The airship pilot needs to drop some ballast or create more dynamic lift, or his craft will slam into the ground.
Long-range airships like the LZ-127 used a mixture of hydrocarbon gases as fuel. This mixture (called Blaugas) was balanced to be just as heavy as air and filled some of the gas cells within the envelope. Consumed fuel would be displaced by air, so no lift adjustment was needed on a long trip.