Like any other attribute, you can specify classes with a JavaScript attribute, seen here:

<button
	class={current === 'foo' ? 'selected' : ''}
	on:click={() => current = 'foo'}
>foo</button>

This is such a common pattern in UI development that Svelte includes a special directive to simplify it:

<button
	class:selected={current === 'foo'}
	on:click={() => current = 'foo'}
>foo</button>

The selected class is added to the element whenever the value of the expression is truthy, and removed when it's falsy.