Crust is made by melting mantle. Small percentages of the mantle melt - the resulting magma is more buoyant and so rises towards the surface. So you can say that the crust is the scum of the Earth!
The main place where new crust, indeed new plate, is created is at mid ocean ridges. This is oceanic crust but over geological time almost all of this is recycled back into the mantle by subduction. Continental crust is different. It is generally too buoyant to be recycled into the mantle by subduction. Once formed it stays on top. And as it still forms today the amount of continental crust has been increasing over geological time. Even so, only about 40% of the Earth's surface is represented by continental crust.
So how is continental crust formed? As it involves melting small amounts of mantle and then for these small amounts to congeal near the Earth's surface we should rephrase the question: where does the important mantle melting happen? There are two key sites. Mantle plumes, the deep structure of "hot spots" are sites of melting. These can erupt sheets of flood basalt lava at the Earth's surface. Examples include the Deccan Traps of India and the Parana basalts of Brazil/Paraguay. These occupy areas of more than 50,000 and 750,000 square kilometres respectively. Far more material may exist at depth (so-called "underplate"), caked on at the base of the old continental crust.
But plumes are only one way to add to the volume of continental crust. At present the main way in which new
continental crust is formed is at subduction zones. Although these are the sites of plate destruction, as oceanic
plates are recycled into the mantle, they are also factories for making new continental crust. This happens
because water entrained in the subduction zone triggers melting in the mantle. This magma is manifest as volcanic
island arcs and cordillera. Island arcs, such as form the eastern rim of the Caribbean, form when subduction happens
beneath oceanic crust. Here a whole suite of new igneous rocks are intruded, creating new crust that is too
buoyant to be subducted. Eventually, over geological time, this island arc is plastered onto the side of an older
continent, adding to its volume. When subduction happens beneath an already existing continent, igneous rocks
thicken it up, manifest as cordilleran mountain ranges. The classic example are the Andes.
The modern continents are made up of crust of all sorts of ages. The oldest crust is over 3.8 billion years
old (examples in southern Africa, Canada and Australia). 
The old crust has been added to and then "remobilised" by
tectonics. Interestingly, the creation of new continental crust has not been a steady process - there are distinct
periods in Earth History when continental crust is preferentially formed. Earth scientists are still not sure
why - could it be that plate tectonics has operated sporadically through time?
The geology of NW Scotland charts a similar pattern as the global picture. Although there are no rocks preserved from the oldest period of continental growth, the Lewisian complex was largely formed in the next one. Much of the Lewisian was formed by magmatism about 2.5 billion years ago. And a major period of reworking, accompanied by melting, happened at about 1.8 billion years ago. The evidence for the next great global pulse of activity at about 1 billion years ago is a little circumstantial. But the Torridonian sediments (1000 - 800 million years old) tell of a major mountain range of this age to the west of modern Scotland. In Canada this mountain building episode is called the Grenvillian where there are major structures of this age. The final key episode about 500 million years ago coincides with the Caledonian mountain building episodes of the British Isles. Effectively the Grampian Highlands represent the new crust of this age - and also the crust of the Midland valley of Scotland and the Southern Uplands. Since then the amount of new crust added to Scotland has been rather small. The only reasonable addition came because of the proto-Iceland mantle plume about 60 million years ago., Mantle melting added magma to form the so-called British Tertiary Igneous Province. These are manifest as the rugged hills of the Cuillins of Skye and other volcanic formations such as the Antrim basalts of northern Ireland. But a lot more material may exist at the base of the crust, underplated onto the ancient foundations of Scotland.
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