Several things in a computer make noises. First of all, the head in a disk drive makes some noise as it moves in and out over the aluminium platters in the drive during disk access. The head is actuated by devices called stepper motors which can rapidly move the head towards the center or edge of the disk. The motor which drives the platter/platters in a hard disk may also make some noise.
There may be one or more fans in a computer for cooling the electronics. The microprocessor (CPU) is likely to have a fan and there will also be a general purpose fan for drawing air through the machine to cool it. Usually there is a temperature sensor, and the fan cuts in and out as the temperature rises above and falls below threshold levels (just like the way an electric cooling fan for the radiator may turn on when a vehicle with the engine running is stationary for any length of time). Alternatively the speed of the fan may be varied, depending on the amount of processing of data which is taking place. It occasionally happens also on desktop computers when a fan gets old, the bearings can wear and the fan becomes noisy.
The power supply may also make some noise. When a current passes through electronic components, sometimes, electric or magnetic fields can cause movement (e,g, if you hold an older style, non switched mode, power adapter up to your ear, you can hear it humming). A sudden demand for power from the supply could cause clicking sounds.
Other clicking sounds can be caused by thermal expansion/contraction as the computer warms/cools (like the way gutters or roofs can creak when the sun comes out).
The old style dial up modem sounds were due to the "tones" which were sent down the line. Digital bits can't be sent directly down a phone line. Instead, various tones or sound frequencies were used to represent "ones" and "zeros".
As regards cooling fans, there is no harm installing a utility on your computer which displays the core temperature of the CPU or (CPUs if the machine is dual core or quad core). I have a utility called core temp installed which displays the temperature on the taskbar. It will power down the machine or display a warning if the temperature exceeds a set value. If you have a laptop, leaving it on a sofa can cause it to overheat, because the air intake may be under the machine and can get blocked. Another tip is to setup a laptop running on battery power so that it goes to sleep after a few minutes of inactivity.
