Before putting your instrument back in its case after playing, do the following...
Use the water key to empty water form the instrument. Blow air through it.
Remove the mouthpiece and slide assembly. Do not take the outer slide off the inner slide piece. Return the instrument to its case.
Once a week, wash the mouthpiece with warm tap water. Dry thoroughly.
Trombone slides occasionally need oiling. To oil your slide, simply...
Rest the tip of the slide on the floor and unlock the slide.
Exposing the inner slide, put a few drops of oil on the inner slide.
Rapidly move the slide back and forth. The oil will then lubricate the slide.
Be sure to grease the tuning slide regularly to prevent it from getting stuck.
Soak the disassembled body and slide in lukewarm, soapy water for 15-20 minutes,.
Scrub with a snake cleaner.
Rinse thoroughly.
Let it dry completely.
Oil the inner slide and grease the tuning slide when reassembling the instrument.
Regular cleaning every 3-6 months prevents buildup.