Low risk
A tap that takes force to turn on or off has scale, a seized spindle or a worn cartridge. Forcing it risks a snapped spindle and a leak.
A tap that rocks on the sink or turns with the handle has a loose fixing underneath: the mounting nut, the washers or a grub screw.
Caution
Water that comes from the handle, the spindle, the swivel or the base, rather than the spout, is escaping past an O-ring, a gland or a washer.
A tap that spits, coughs or runs in bursts has air in the pipe: an airlock after work or a supply that has been interrupted.
A single tap that squeals, hums or shakes as water flows has a worn washer or cartridge, a loose jumper or pressure that is too high for it.
An outside tap that leaks at the spindle, runs on after you turn it off or will not turn at all has a worn gland or washer, scale or frost damage.
Describe the job and get a fixed price from a local plumber.