How are variant prices and surcharges reflected in the product detail price that the customer sees?

There are two display options for variant surcharge values on the product detail page.
Both options are controlled via Settings>Store Settings>Storefront settings. Check the box to display price changes when a variant is selected.

When a customer selects a variant with a negative or positive surcharge, this is immediately reflected in the price that the customer sees assuming you have the 'Our Price' field entered with a price and activated via your theme or product detail page design.

This means that the surcharge price does not show on the variant menu any more as only the main price can be adjusted (i.e. only the variant name will show).

The quantity discount amounts will also be adjusted to reflect the surcharge change.

You can adjust the surcharge amount by visiting Inventory>Products, selecting the product to go into the product detail and scroll down to the variants section and add a value in the Surcharge column.
Standard variant surcharge display on variant drop down menu. In this case, the main price display will not change when a variant with surcharge value is selected. On the variant menu, you can activate the surcharge display which will look like;
Size Medium + $12