Learn how to take apart the trombone trigger so that you can thoroughly clean the inside of the mechanism. Often, a sticking trigger is the result of gunk and debris getting inside the mechanism. Taking the trigger apart will allow you to get into the small working parts and clean the trigger thoroughly. The top of the trigger may be removed like a valve cap by turning it counterclockwise to remove it from the trombone. Since you only need to do this once or twice a year, it is often best to take your horn to a professional to clean out your trigger.
Inspect the outside of the trombone trigger for any visible damage such as dents or loose parts. If the trombone trigger feels loose, you may need to take the trombone apart and restring the rotor. This can be done by threading a string with a knot in the end through the hole in the top of the rotor and then threading around the rotor to mimic the position of the original thread. This process takes some expertise, but with practice you will learn to thread the rotor properly.
Oiling is probably the easiest fix for a trombone trigger that isn't working. Remove the tuning slide on the back of the trombone by pulling it straight back. Place the slide aside and pour five to eight drops of oil down the tube that the rotor is attached to. Pump the trigger several times while aiming the bell of the trombone toward the ground. This will ensure that oil is distributed evenly throughout the rotor. In most cases, this will fix a rotor that is sluggish. If oiling doesn't work, give your trombone a cleaning in the bathtub using a half cup of dishwashing liquid. Use a snake to clean out the insides and thoroughly dry and grease the trombone slides when finished.
You may need to purchase a new rotor and install it yourself if you have the knowledge, or have a professional install it for you. Order the rotor parts that correspond to the make and model of your horn and simply replace the old parts with the new ones. Double-check that the thread that connects the rotor to the trigger is installed correctly by activating the trigger and seeing if it pulls upon the rotor properly. When this is done correctly, your rotor should move smoothly and without resistance.