Most of the time laminators will steam right along, requiring little attention. But at all times it's a good idea to keep it clean so that dust and grit don't get inside and spoil the lamination: also, excessive grit and dirt may get into the moving parts, which eventually will do no good at all.
For external cleaning: turn the machine off and unplug it. Let it cool off for twenty minutes or so. If the machine is merely dusty, a damp cloth is all that's needed. If there is something tougher than that, use a mild detergent, diluted well. DO NOT use alcohol, petroleum-based cleansers, or harsh abrasives. Be especially careful not to let anything get inside the machine: cover the input & output slots with a towel or something.
If something jams inside the machine while operating, it may be possible to clear it out without calling for service. Unplug the machine and wait twenty minutes: remove the cover (if this is a difficult matter then best leave it to the experts). If the jam is visible, and if it will come out with just gentle pressure, then it will probably be all right to remove it: but almost certainly some residue will remain on the rollers or other parts of the mechanism which will eventually bung things up.
In this context, if you've been using the laminator for foil stamping or single-sided lamination, there is an increased possibility that fluid will have been deposited on the rollers, or that bits of cardboard or other foreign materials are loose inside.
For all but the cheapest laminators - which may be more economical to replace than repair (it happens!) - a regular professional servicing is an idea that will pay for itself. Hang on to the purchase documents, packing slips and material, and manuals - anything that comes with the machine - in case warranty or other issues come up when the machine konks out. For very expensive machines the manufacturer's accredited service reps should be used.
And in self-defense — make sure that all users of the machine know what they are doing!