Whenever moving a clock, please remove the pendulum and weights.  Weights swinging in a case can cause great damage.  The pendulum and movement may be damaged if the pendulum is allowed to swing wildly.  Many antique tall case clock movements and dials just rest on the side rails of the case.  Failure to handle these clocks correctly when moving can result in severe damage to the clock.

Do not "help" the weights when winding the clock.  The weights hang from the clock without help every moment between windings just fine.  If a chain becomes slack the chain may come off its sprocket.  If a cable becomes slack it may jump a groove or tangle around its winding drum.  In bad cases the cable may even saw partially through itself resulting in expensive repair(s).  While well intentioned, helping weights is a bad idea.

A clock should rest firmly on the surface supporting it.  Be it a floor, a table, a shelf, or a mantle, if the clock can rock it may not run correctly.  When setting up a clock, try to get it a close to level as possible.  If tilted too far front to back, the pendulum and / or weights may rub against each other of case parts, stopping the clock.  The clock should tick evenly when running.

If your clock has frayed cables, chains that jump and jam on the sprockets, or a spring that feels loose and tries to jump back when you wind the clock your clock needs attention.  A falling weight can do quite a bit of damage to the clock, and in tall clocks even break through and damage the floor under the clock.  If the "click" which holds the spring fails, the winding key can spin backwards very fast.  A person can't react quickly enough to get their fingers out of the way.  I've lost part of a fingernail to a clock spring that got loose while winding, others have ended up with torn flesh and broken fingers.  Please don't ignore warning signs of spring problems.

Never use any spray lubricant on a clock.  There are a number of good synthetic oils available that are known to be good clock oils.  Most spray lubricants turn gummy over time, and leave residue that attracts dust and airborn particles to moving parts, increasing wear.  When dealing with clocks and watches, too much oil is worse than too little.

Unless you know it is OK, turn hands clockwise only.  Most modern mechanical clocks can have the hands turned in either direction.  American time and strike clocks with a wire hanging down to syncronise the strike can not be turned backwards.  French clocks and carriage clocks with a directional arrow must ONLY be turned in the direction of the arrow.  When moving the hands, always allow the chime (if a chime clock) and strike to complete before continuing to advance the hands.  Use good judgement.  If it feels as though the hand should not be moved past some point, do not force it.

Your clock case is a piece of furniture.  Dusting, cleaning, and occasional waxing with good quality furniture polish or wax will keep your clock looking good and help it to run well.