I would first emphasise that time had only just become important when most of the clocks you see on this site were made, so you shouldn't expect modern day atomic accuracy from any of them. If you want something accurate, get a £400 Seiko quartz watch (which is what I have for reference to help me regulate my antique clocks). it's even more accurate than my £2,000 mechanical Omega.
Only once it's cleaned properly and correctly set in beat, can a mechanical antique clock be regulated for consistent accuracy. See my pages on CLEANING and SET UP for more about these pre-requisites. Of the spring-driven clocks (fusée chronometers excepted), you should be looking for relative accuracy across the week. When a spring is fully wound, it stores a great deal of energy so will tend to drive a clock very well. By the end of the week, however, the mainspring is a little under half wound and so it's stored power is considerably reduced (and the clock may run a tad slower).
The fusée movement tries to counteract this effect by exerting greater leverage when the spring is weaker, and less leverage when it is stronger. The difference is very small indeed but the first lesson to learn about regulating your clock is to leave it alone for a few days after winding it to see how it performs over a few days.
Temperature can also affect a clock's accuracy because heat causes metal to expand so if the pendulum rod is metal, it will be fractionally longer in warmer weather than in colder weather. The pendulum length is key to regulating a clock; the shorter it is the quicker the clock will run. So on a winter's night, a clock might run faster than it does on a summer's day.
To counteract this effect, the pendulum rod on some clocks (Vienna regulators for example) is wooden - wood is much less susceptible to temperature expansion and contraction. Many French "Four glass" clocks have a steel pendulum shaft but the bob incorporates two glass phials filled with mercury - in hotter weather the steel rod expands but the mercury also rises in the phial, lifting the centre of gravity. Other clocks have a several rods of different metals that are fastened together in such a way as to pull in opposite directions to cancel each other out (the gridiron style on a German springer wall clock). Carriage clocks have a balance wheel instead of a pendulum but use a bi-metal design to the same effect. So there are various scientific ways to address the problem of expansion.
But if you can raise the bob by turning a screw under or in it, you'll quickly discover that the clock runs more quickly. Many clocks have the letters S (for slower) and F (for faster) engraved or stamped somewhere to on the pendulum bob to help you. These letters almost always appear on the platform escapement of a carriage clock, too - open the back door to adjust the lever while looking down through the glass window on top but only make a very, very small adjustment. On 400-day clocks, the same symbols with arrows are also visible on the top of the rotating 'four balls' bob (or on one of the two weights on the flat disc version). And on bracket clocks, there's often a subsidiary dial on the front at the top marked S and F so you only need to turn the small hand to adjust it.
But it's not always that easy. If you have only just bought the clock and it came from a less than reputable source (like 'fleabay'!), it may run too fast or too slow because someone has supplied the wrong pendulum. The bob could be too heavy or the rod might be too short so no amount of adjustment will correct it - it needs a replacement pendulum. Or if it's a 400 day (torsion) clock, the wrong suspension might have been fitted and it's too thick or too thin, or just buckled. If it's gaining or losing an hour or more a day, then this is almost certainly the cause. But don't worry, I can sort that out for you quite inexpensively and can probably even source the right part within a week if I don't already have one to swap for it.
So if you try these tips but still can't get your clock to keep reasonable time yourself, email me with details and I will happily take a look at it for you.