How is capacitance increased/decreased?
There are two commonly used methods.
Mechanically Variable Capacitors
The most traditional technique is to make a capacitor from a stack of sector-like fixed plates, and moving plates on a rotary shaft, and rotate that for more or less overlap with the fixed plates.  This is what you typically found in traditional broadcast receivers - eg the classic 365 pF AM tuning capacitor. Often there would be multiple distinct variable capacitors on a common shaft, for example to tune both a tracking preselector filter and the local oscillator, or for use on bands of extremely different frequency.
A variation of this technique sometimes used for trimmer capacitors is to have a set of plates which are compressed to change spacing by a screw (though some better trimmers are just miniature versions of rotary plate capacitors).  There'a also the physics lecture apparatus where very large plates would stand on some sort of slider which could vary their spacing over substantial distance.
Electronically Variable Capacitors
The second major technique is to exploit how semiconductor diode junctions vary in capacitance with applied DC vias voltage.  There are specific varactor diodes made to be optimal for this, but some other types have sufficiently useful behavior to be sometimes exploited, too.  This technique is very useful for making a voltage controlled oscillator such as might be used in a Phase Locked Loop.  It also shows up in some simpler electronically tuned radios (eg dirt-cheap &quot;pound shop&quot; radios) and is sometimes chosen for fairly sophisticated gear because it permits using a potentiometer as a tuning control, which can be more easily remote mounted on a front panel and does not suffer from hand capacitance (or LO radiation) the way unshielded physically variable capacitors do, since the actual capacitive element and surrounding tuned circuit is buried inside and only a DC tuning voltage is anywhere near the user's hand or front panel.
There are likely other methods as well, but these are the most common.