It is important that you exercise great care when handling your trombone. The slide is exceptionally delicate, and the slightest knock could cause a dent which might hamper its movement.
The slide will require regular lubrication. You will need to apply a little slide cream or oil to the boot area of the slide. The boot is at the end of the slide, so you should exercise great caution to ensure the slide does not slip off the trombone.
As with valve instruments, once you have finished playing your trombone, you should ensure that all moisture is removed from the inside of the horn. Open the water keys and blow through the instrument. Wipe the exterior to remove oils from your fingers, and put the instrument back in its case. Not only does this protect your instrument from damage, but it also helps to keep it clean. Never place items in the case with your instrument which are not meant to be there. When the lid is closed, they may press against your instrument and damage its delicate slides.
If the mouthpiece becomes stuck, again, don’t panic, and don’t try to force it off. Take it to your local music shop to remove. As with valve instruments, the problem of stuck mouthpieces is usually caused by incorrect insertion. The correct method of inserting a mouthpiece is to lie the mouthpiece in the receiver and apply a tiny amount of pressure to help it stay in place. You may give a slight twist, with the emphasis very much on slight. Excessive twisting will almost certainly result in the mouthpiece getting stuck.
You will need to check the tuning slide from time to time to ensure that it moves freely, lubricating it with slide grease as necessary.
As with valve instruments, the interior of your trombone requires regular cleaning which should be carried out at least every three months. You may also wish to consider an occasional chemical clean (contact your local music store for more information) to bring out the best of your instrument and make it look just like new!