Learn Finnish: Hän laiskottelee koko viikonlopun mökkeilemällä saaressa. - He lazes around all weekend by staying at a cottage on the island.

This is the third infinitive in the adessive case (-mällä or -malla). It expresses the means or method by which an action is done, translating perfectly to the English structure "by doing" something. Here, the base verb is mökkeillä (to spend time at a cottage).

Why is koko viikonloppu in the genitive-like accusative form (koko viikonlopun)?

When expressing a duration of time that an action spans completely, Finnish uses the total object form. For singular nouns, this looks identical to the genitive case. It shows that the action of lazing around consumes the entire duration of the weekend.

English says "on the island", so why does Finnish use the inessive case saaressa (in the island) rather than saarella?

Finnish traditionally uses the inessive case (-ssa / -ssä) for islands when talking about being there generally, as if the island is an environment you are immersed in. You might hear saarella in some contexts or regions, but saaressa is the standard way to express this.

Both laiskottelee and mökkeilemällä look like they are derived from simpler words. How are these verbs formed?